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Integrable representations for toroidal extended affine Lie algebras

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0 Published in 2019 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2018.11.003

Abstract: Let $\fg$ be any untwisted affine Kac-Moody algebra, $\mu$ any fixed complex number, and $\wt\fg(\mu)$ the corresponding toroidal extended affine Lie algebra of nullity two. For any $k$-tuple $\bm{\lambda}=({\lambda}_1, \cdots, {\lambda}_k)$ of weights of $\fg$,… read more here.

Keywords: extended affine; lie algebra; affine lie; toroidal extended ... See more keywords

Affine Lie superalgebras

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0 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2020.10.039

Abstract: Abstract In 1986, Van de Leur introduced and classified affine Lie superalgebras. An affine Lie superalgebra is defined as the quotient of certain Lie superalgebra G defined by generators and relations, corresponding to a symmetrizable… read more here.

Keywords: lie super; lie superalgebras; affine lie; lie ... See more keywords

Vertex algebras and extended affine Lie algebras coordinated by rational quantum tori

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0 Published in 2021 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2020.11.010

Abstract: Abstract Let sl N ˆ ( C q ) be the core of extended affine Lie algebra of type A N − 1 coordinated by the rational quantum 2-torus C q . In this paper,… read more here.

Keywords: algebra; affine lie; lie; coordinated rational ... See more keywords

Extended affine Lie superalgebras and their affinizations

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0 Published in 2019 at "Communications in Algebra"

DOI: 10.1080/00927872.2018.1448840

Abstract: Abstract Extended affine Lie superalgebras are super versions of the defining axioms of extended affine Lie algebras or more generally invariant affine reflection algebras. This class includes finite dimensional basic classical simple Lie superalgebras and… read more here.

Keywords: lie superalgebras; affine lie; lie; superalgebras affinizations ... See more keywords

Combinatorial bases of standard modules of twisted affine Lie algebras in types A2l−1(2) and Dl+1(2) : rectangular highest weights

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2 Published in 2022 at "Communications in Algebra"

DOI: 10.1080/00927872.2023.2196337

Abstract: We consider the standard modules of rectangular highest weights of affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$. By using vertex algebraic techniques we construct the combinatorial bases for standard modules and their principal subspaces… read more here.

Keywords: lie algebras; standard modules; highest weights; algebras types ... See more keywords

Groups of Extended Affine Lie Type

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1 Published in 2019 at "Publications of the Research Institute for Mathematical Sciences"

DOI: 10.4171/prims/55-3-5

Abstract: We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame… read more here.

Keywords: affine lie; lie; extended affine; groups extended ... See more keywords