Automorphism group and representation of a twisted multi-loop algebra

Cui, Chen; Lian, Hai Feng; Tan, Shaobin

doi:10.1007/s10114-010-8062-2

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Cited by 3 publications

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“…The similar twisted multi-loop algebra of type A 1 was studied by [3,6]. From [7,8,10], one can see that the Tits-Kantor-Koecher algebra G (T (S)) (which is obtained from a Jordan algebra T (S) with semilattice S in Z 2 by using the Tits-Kantor-Koecher construction) is spanned by…”

Section: Introductionmentioning

confidence: 98%

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Wakimoto modules for twisted multi-loop algebra of type A 1 × A 1

Lan¹,

Kong

Jiang³

2015

Front. Math. China

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Section: Introductionmentioning

confidence: 98%

“…In Section 3, we consider the structure of Fock space and construct a class of submodules. In Section 4, we extend V to be an L -module, and we prove that V 1 is an irreducible submodule of V. The construction of these modules is motivated by [3,4,8].…”

Section: Introductionmentioning

confidence: 99%

Wakimoto modules for twisted multi-loop algebra of type A 1 × A 1

Lan¹,

Kong

Jiang³

2015

Front. Math. China

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The structures for the loop-Witt algebra

Tang

Zhang

2012

Acta. Math. Sin.-English Ser.

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Automorphism Group of a Class of Gradation Shifting Toroidal Lie Algebras

2010

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Let [Formula: see text] be the ring of Laurent polynomials in commuting variables. As a generalization of the toroidal Lie algebra, the gradation shifting toroidal Lie algebra [Formula: see text] is isomorphic to the corresponding (centerless) toroidal Lie algebra so(n, ℂ) ⨂ A of type B or D as a vector space, with the Lie bracket twisted by n fixed elements E1,…,En from A. In this paper, we study the automorphisms of the gradation shifting toroidal algebra [Formula: see text], which is proved to be closely related to a class of subgroups of GL(n,ℤ), called the linear groups over semilattices. We use the linear group over a special semilattice to determine the automorphism group of the gradation shifting toroidal algebra [Formula: see text], which extends our earlier work.

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Automorphism group and representation of a twisted multi-loop algebra

Cited by 3 publications

References 8 publications

Wakimoto modules for twisted multi-loop algebra of type A 1 × A 1

Wakimoto modules for twisted multi-loop algebra of type A 1 × A 1

The structures for the loop-Witt algebra

Automorphism Group of a Class of Gradation Shifting Toroidal Lie Algebras

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