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In the theory of Lie algebras, an sl2-triple is a triple of elements of a Lie algebra that satisfy the commutation relations between the standard generators
Sl2-triple
statement of Jacobson–Morozov relies on the following preliminary notions: an sl2-triple in a semi-simple Lie algebra g {\displaystyle {\mathfrak {g}}} (throughout
Jacobson–Morozov_theorem
Unitary representations of a Lie group
representations split as a sum of eigenspaces of H), and {H, X, Y} is an sl2-triple, which means that they satisfy the relations [ H , X ] = 2 X , [ H , Y
Representation theory of SL2(R)
Representation_theory_of_SL2(R)
conjugacy class of principal subalgebras, each of which is the span of an sl2-triple. Bourbaki, Nicolas (2005) [1975], Lie groups and Lie algebras. Chapters
Principal_subalgebra
into an sl2-triple {e,h,f} and all such triples are conjugate by ZG(e), the centralizer of e in G. Together with the representation theory of sl2, this
Nilpotent_orbit
Concept in mathematics
ISBN 978-3-540-67827-4. Affine Weyl group Finite Coxeter group Hasse diagram Linear algebraic group Nilpotent orbit Root system sl2-triple Weyl group
Special_linear_Lie_algebra
Hodge decomposition the triple of operators { Π , L , Λ } {\displaystyle \{\Pi ,L,\Lambda \}} descend to give an sl2-triple on the de Rham cohomology
Kähler_identities
Associative algebra generalizing the Virasoro algebra
nilpotent element e. By the Jacobson-Morozov theorem, e is part of a sl2 triple (e, h, f). The eigenspace decomposition of ad(h) induces a Z {\displaystyle
W-algebra
Solution to x*x + y*y + z*z = 3xyz
\end{cases}}} where (p, q, r) is a Markov triple. Let tr denote the trace function over matrices. If X and Y are in SL2( C {\displaystyle \mathbb {C} } ), then
Markov_number
000 units, with production ending in 1974. Leicaflex SL2/SL2 MOT (1974–1976) – The Leicaflex SL2 is the third and the last Leicaflexes ever made. This
List_of_Leica_Camera_models
Representation of the symmetry group of spacetime in special relativity
ϵ i j k K k , {\displaystyle [J_{i},K_{j}]=i\epsilon _{ijk}K_{k},} the triple (K1, K2, K3) ≡ K is a vector operator and the Wigner–Eckart theorem applies
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Rational function of the form (az + b)/(cz + d)
{\displaystyle {\mathfrak {H}}(z)} mapping a triple ( z 1 , z 2 , z 3 ) {\displaystyle (z_{1},z_{2},z_{3})} to another triple ( w 1 , w 2 , w 3 ) {\displaystyle
Möbius_transformation
of order 32, and the quotient by this subgroup is isomorphic to the group SL2(3) of order 24. It also acts on the Hesse pencil of elliptic curves, and
Hessian_group
1979 single by KC and the Sunshine Band
During the weeks that the song was number one on the UK Singles Chart, SL2's "On a Ragga Tip", Guns N' Roses' "Knockin' on Heaven's Door", Shut Up &
Please Don't Go (KC and the Sunshine Band song)
Please_Don't_Go_(KC_and_the_Sunshine_Band_song)
below. The 3′ UTR of Alphacoronaviruses consists of two small hairpins (PK-SL2) which can form an alternate conformation (PK-SL1) where the loop region
Coronavirus_3′_UTR
indicates a 250 SX East/250 SX West combination event. B (TC) indicates a Triple Crown event. Justin Barcia opened the season with his second consecutive
2020 AMA Supercross Championship
2020_AMA_Supercross_Championship
MBTA Commuter Rail line
Branch, from the Penn Central's bankruptcy trustees. Ridership on the line tripled from 1982 to 1990. From the start of MBTA operations, Franklin was the
Franklin/Foxboro_Line
City in Massachusetts, United States
South Station and runs through the Waterfront Tunnel, along with the SL1 and SL2 routes, to Silver Line Way, continuing with the SL1 through the Ted Williams
Chelsea,_Massachusetts
Football league season
National Premier Leagues WA Women format. It was played over 21 rounds as a triple round-robin, followed by an end of season Top 4 Cup competition. Source:
2025_Football_West_season
Open convex self-dual cones
Mathématiciens (Nice, 1970), Tome I, Gauthier-Villars, pp. 279–283 Lang, S. (1985), SL2(R), Graduate Texts in Mathematics, vol. 105, Springer-Verlag, ISBN 978-0-387-96198-9
Symmetric_cone
Seaport district in Boston, Massachusetts
as a test track. There is public transit access via the MBTA Silver line SL2 route. 2km 1.2miles 4 3 2 1 The public facilities, operated by the Massport
Port_of_Boston
Mathematical transform that expresses a function of time as a function of frequency
transformations, which can be visualized as the action of the special linear group SL2(R) on the time–frequency plane, with the preserved symplectic form corresponding
Fourier_transform
Eisenstein series E(τ,s) over a fundamental domain D of the modular group SL2(Z) acting on the upper half plane ∫ D f ( τ ) g ( τ ) ¯ E ( τ , s ) y k −
Rankin–Selberg_method
Lie algebra classification
group of order 2. Type VIII: The Lie algebra sl2(R) of traceless 2 by 2 matrices, associated to the group SL2(R). It is simple and unimodular. The simply
Bianchi_classification
123rd season of competitive spccer in Western Australia
National Premier Leagues WA Women format. It was played over 21 rounds as a triple round-robin, followed by an end of season Top 4 Cup competition. Source:
2023_Football_West_season
American mathematician
Jean; Gamburd, Alexander. "Uniform expansion bounds for Cayley graphs of SL2(Fp)". Annals of Mathematics 167 (2008), pages 625-642. MR 2415383 Breuillard
Alexander_Gamburd
Generalized manifold
2-dimensional subspace in F73 and hence gives rise to a homomorphism Ψ of Γ1 into SL2(F7), a group of order 16·3·7. On the other hand, the stabiliser of a vertex
Orbifold
Mathematical theory
example of the Langlands classification, see the representation theory of SL2(R). There are several minor variations of the Langlands classification. For
Langlands_classification
Science behind the motion of bicycles and motorcycles
August 19, 2004". Retrieved 2008-06-23. "Velo News: Specialized Roubaix SL2 goes wide, June 27, 2008". 27 June 2008. Retrieved 2008-06-27. "Design News:
Bicycle and motorcycle dynamics
Bicycle_and_motorcycle_dynamics
Carter the Unstoppable Sex Machine (24 October) Mariah Carey (24 October) SL2 (31 October) Congress (31 October) Moby (31 October) Crowded House (7 November)
List of performers on Top of the Pops
List_of_performers_on_Top_of_the_Pops
World War I air campaign
lost with all hands. Two Army Zeppelins bombed London on 7/8 September, SL2 dropped bombs on the Isle of Dogs, Deptford, Greenwich and Woolwich, and
German bombing of Britain, 1914–1918
German_bombing_of_Britain,_1914–1918
MBTA Commuter Rail line
frequent cancellations, a June 2016 count showed that ridership had nearly tripled from 2012. While the line is still among the least-used on the MBTA Commuter
Fairmount_Line
drivers registered for the event; however an important absentee was the triple champion Germán Quiroga. Additionally, the most popular driver winner, Jorge
2012_NASCAR_Toyota_Series
Sports season
National Premier Leagues WA Women format. It was played over 21 rounds as a triple round-robin, followed by an end of season Top 4 Cup competition. Source:
2021_Football_West_season
Football league season
National Premier Leagues WA Women format. It was played over 21 rounds as a triple round-robin, followed by an end of season Top 4 Cup competition. Source:
2024_Football_West_season
Czech geologist and planetologist JPL · 26970 26971 Sezimovo Ústí 1997 SL2 Sezimovo Ústí, a town in southern Bohemia of the Czech Republic JPL · 26971
Meanings of minor-planet names: 26001–27000
Meanings_of_minor-planet_names:_26001–27000
Sports season
National Premier Leagues WA Women format. It was played over 21 rounds as a triple round-robin, followed by an end of season Top 4 Cup competition. Source:
2022_Football_West_season
SL2 TRIPLE
SL2 TRIPLE
Female
Irish
Irish Gaelic name SLÃINE means "health."
Surname or Lastname
English (chiefly West Midlands)
English (chiefly West Midlands) : nickname for a cunning or crafty individual, from Middle English sligh ‘sly’ (earlier slegh, from Old Norse slǽgr).
Surname or Lastname
English
English : variant of Sly.
Male
Norse
Old Norse name composed of the name of the god Thor and the word gÃsl "arrow, shaft," hence "Þórr's arrow."
Surname or Lastname
English
English : variant spelling of Sly.
Surname or Lastname
English
English : variant of Sly, with the addition of Middle English man ‘man’.Dutch : from Middle Dutch slie, sly ‘tench’ + man ‘man’, occupational name for a catcher or seller of these fish.
Surname or Lastname
English
English : topographic name for someone who lived near a swamp or bog, from Old English slÅh ‘slough’, or a habitational name from one of the various places named with this word, for example Slough in Berkshire.
Female
Scottish
Scottish form of Irish Gaelic Sláine, SLÀINE means "health."
Boy/Male
German
Prince; Angelic; Angel; Sly Attractive
Surname or Lastname
English
English : occupational name for a slaughterer of animals, from Middle English slahter (an agent derivative of slaht ‘killing’).English : topographic name from Middle English sloghtre ‘boggy place’, or a habitational name from a place named with this term (Old English slÅhtre), for example Upper and Lower Slaughter in Gloucestershire.English : topographic name for someone who lived by a blackthorn or sloe, Old English slÄhtrÄ“ow.
Surname or Lastname
English
English : nickname from Middle English sleght, sleight, slyght ‘cunning’, ‘artfulness’.English : topographic name from Middle English sleyte ‘level field’ (Old Norse slétta) or from Middle English sleyte ‘sheep pasture’.
Boy/Male
Shakespearean
King Richard III' Christopher Urswick, a priest. 'The Taming of the Shrew' Christopher Sly, a...
Surname or Lastname
English
English : topographic name from Middle English slape ‘slippery, miry place’, or a habitational name from any of the places named with this word (Old English slǣp), as for example Slape in Dorset or Sleap in Shropshire.
Surname or Lastname
English (southern)
English (southern) : topographic name from Middle English slade ‘small valley’, or a habitational name from any of the places named with this word (Old English slæd), for example in Devon and Somerset, or Slad in Gloucestershire.
Surname or Lastname
English
English : elaborated form of Sly, with the addition of Middle English man ‘man’.
Surname or Lastname
English
English : variant of Sly, with the addition of Middle English man ‘man’.
Male
English
Pet form of English Sylvester, SLY means "from the forest."
Surname or Lastname
English
English : from a medieval personal name, Aslak, found in Norfolk; it is from the Old Norse personal name Ãslákr, composed of the elements áss ‘god’ + leikr ‘game’, ‘fight’.
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name for someone from any of various minor places in northern France named from Old French aunaie ‘alder grove’.Irish : Anglicized form, influenced by the Norman name, of Gaelic Ó Dubhshláine ‘descendant of Dubhshláine’, a personal name composed of the elements dubh ‘black’ + slán ‘challenge’, ‘defiance’. MacLysaght, however, suggests that this element may be from the Sláinge river.
Female
Swedish
Swedish form of Old Norse Ãslaug, Ã…SLÖG means "God-betrothed woman."
SL2 TRIPLE
SL2 TRIPLE
Boy/Male
Tamil
Yeshwin | யேஷà¯à®µà¯€à®¨
Boy/Male
Teutonic
Free.
Girl/Female
American, Arabic, Australian, British, English, Hebrew, Italian, Muslim, Sindhi
Purity; To Desire; Sea of Bitterness; Sea of Sorrows; Sorrow; Lady with Fair Complexion; Name of the Wife of the Prophet Muhammad
Boy/Male
German American Welsh Irish English
Spear.
Girl/Female
Indian
Intelligent, Pure
Boy/Male
English
Hard boar.
Boy/Male
Australian, German, Norwegian, Swedish
Stone
Girl/Female
Hindu, Indian, Traditional
Nature
Boy/Male
Christian & English(British/American/Australian)
Patriotic
Surname or Lastname
English
English : variant spelling of Callaway.
SL2 TRIPLE
SL2 TRIPLE
SL2 TRIPLE
SL2 TRIPLE
SL2 TRIPLE
a.
Stealthy; sly.
v. t.
Done with, and marked by, artful and dexterous secrecy; subtle; as, a sly trick.
a.
Deceitful; cunning; sly.
a.
Cinning; sly.
a.
Sly; crafty; cunning; artful.
n.
A sly, cunning fellow.
a.
Crafty; cunning; sly; as, vafrous tricks.
a.
Sly.
adv.
Slyly.
a.
Arch; cunning; sly.
v. t.
Artfully cunning; secretly mischievous; wily.
a.
Sly; cunning; insinuating; deceitful.
v. t.
To slay.
a.
Fawning and deceitful; sly.
n.
A sly or artful person.
v. t.
Dexterous in performing an action, so as to escape notice; nimble; skillful; cautious; shrewd; knowing; -- in a good sense.
a.
Secret; clandestine; sly.
adv.
In a sly manner; shrewdly; craftily.
a.
Crafty; sly; artful; designing; deceitful.
v. t.
Light or delicate; slight; thin.