scholarly journals Rigged configuration descriptions of the crystals B(∞) and B(λ) for special linear Lie algebras

2017 ◽  
Vol 58 (10) ◽  
pp. 101701 ◽  
Author(s):  
Jin Hong ◽  
Hyeonmi Lee
Keyword(s):  
Lie Algebras ◽  
Special Linear ◽  
Rigged Configuration

Orthogonal decompositions of Lie algebras over finite commutative rings

2021 ◽  
pp. 2350006
Author(s):  
Songpon Sriwongsa
Keyword(s):  
Commutative Ring ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Commutative Rings ◽  
Orthogonal Decomposition ◽  
Necessary Condition ◽  
Special Linear ◽  
Orthogonal Lie Algebra ◽  
Orthogonal Decompositions ◽  
Finite Commutative Ring

Let [Formula: see text] be a finite commutative ring with identity. In this paper, we give a necessary condition for the existence of an orthogonal decomposition of the special linear Lie algebra over [Formula: see text]. Additionally, we study orthogonal decompositions of the symplectic Lie algebra and the special orthogonal Lie algebra over [Formula: see text].

scholarly journals GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250046 ◽  
Author(s):  
YURI BAHTURIN ◽  
MATEJ BREŠAR ◽  
MIKHAIL KOCHETOV
Keyword(s):  
Abelian Group ◽  
Lie Algebras ◽  
Vector Spaces ◽  
Closed Field ◽  
Dimensional Vector ◽  
Linear Transformations ◽  
Special Linear ◽  
Infinite Dimensional ◽  
Group Gradings ◽  
Arbitrary Abelian Group

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.

Finite gradings of special linear Lie algebras

2012 ◽  
Vol 185 (2) ◽  
pp. 282-299
Author(s):  
A. A. Zolotykh ◽  
P. A. Zolotykh
Keyword(s):  
Lie Algebras ◽  
Special Linear

Invariant Symmetric Bilinear Forms and Derivation Algebras of Unitary Lie Algebras

2016 ◽  
Vol 23 (03) ◽  
pp. 361-384 ◽  
Author(s):  
Yelong Zheng ◽  
Jiwen Gao ◽  
Zhihua Chang ◽  
Yun Gao
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Associative Algebra ◽  
Bilinear Forms ◽  
Special Linear ◽  
Algebra Over A Field

Invariant symmetric bilinear forms and derivation algebras of a unitary Lie algebra L over R are characterized: ℬ(L) ≅ (R+/([R,R] ∩ R+))* and Der (L) = Inn (L)+ Der (L)0 = Inn (L)+ SDer (R), which recover what of the special linear Lie algebra and Steinberg Lie algebra over R, where R is a unital involutory associative algebra over a field 𝔽.

scholarly journals Adjoint representations for SU(2), su(2) and sl(2)

2017 ◽  
Vol 27 (5) ◽  
pp. 74
Author(s):  
Saad Owaid ◽  
Zainab Subhi
Keyword(s):  
Lie Algebras ◽  
Lie Group ◽  
Vector Spaces ◽  
Linear Matrix ◽  
Unitary Matrix ◽  
Direct Sums ◽  
Special Linear ◽  
The Matrix

This work, presents four kinds of adjoint representations for the special unitary matrix Lie group SU(2) and the special unitary, special linear matrix Lie algebras su(2) and sl(2). In the first two we assume the vector spaces as the matrix Lie algebras su(2) and sl(2), later cases obtained by exploiting the action of su(2) and sl(2)  on themselves. Also, we compute their direct sums. The results have been displayed as Tables in a nice form.

scholarly journals Monomial realization of crystal bases for special linear Lie algebras

2004 ◽  
Vol 274 (2) ◽  
pp. 629-642 ◽  
Author(s):  
Seok-Jin Kang ◽  
Jeong-Ah Kim ◽  
Dong-Uy Shin
Keyword(s):  
Lie Algebras ◽  
Crystal Bases ◽  
Special Linear

scholarly journals Nakajima Monomials and Crystals for Special Linear Lie Algebras

2007 ◽  
Vol 188 ◽  
pp. 31-57 ◽  
Author(s):  
Hyeonmi Lee
Keyword(s):  
Lie Algebras ◽  
Young Tableau ◽  
Special Linear ◽  
Highest Weight ◽  
Nakajima Monomials

AbstractNakajima introduced a certain set of monomials realizing the irreducible highest weight crystals B(λ). The monomial set can be extended so that it contains crystal B(∞) in addition to B(λ). We present explicit descriptions of the crystals B(∞) and B(λ) over special linear Lie algebras in the language of extended Nakajima monomials. There is a natural correspondence between the monomial description and Young tableau realization, which is another realization of crystals B(∞) and B(λ).

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