Module structure of the center of the universal central extension of a genus zero Krichever–Novikov algebra

Cox, Ben

doi:10.1016/j.jalgebra.2016.06.038

Cited by 2 publications

References 25 publications

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On the module structure of the center of hyperelliptic Krichever–Novikov algebras II

Cox

Guo

Im³

et al. 2019

Communications in Algebra

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Let R := R 2 (p) = C[t ±1 , u : u 2 = t(t − α 1 ) · · · (t − α 2n )] be the coordinate ring of a nonsingular hyperelliptic curve and let g ⊗ R be the corresponding current Lie algebra. Here g is a finite dimensional simple Lie algebra defined over C andIn earlier work, Cox and Im gave a generator and relations description of the universal central extension of g ⊗ R in terms of certain families of polynomials P k,i and Q k,i and they described how the center Ω R /dR of this universal central extension decomposes into a direct sum of irreducible representations when the automorphism group was the cyclic group C 2k or the dihedral group D 2k . We give examples of 2n-tuples (α 1 , . . . , α 2n ), which are the automorphism groups G n = Dic n , U n ∼ = D n (n odd), or U n (n even) of the hyperelliptic curvesgiven in [CGLZ17]. In the work below, we describe this decomposition when the automorphism group is U n = D n , where n is odd.

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On the module structure of the center of hyperelliptic Krichever–Novikov algebras II

Cox

Guo

Im³

et al. 2019

Communications in Algebra

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On the module structure of the center of hyperelliptic Krichever-Novikov algebras

Cox¹,

Im²

2018

Representations of Lie Algebras, Quantum Groups and Related Topics

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We consider the coordinate ring of a hyperelliptic curve and let g ⊗ R be the corresponding current Lie algebra where g is a finite dimensional simple Lie algebra defined over C. We give a generator and relations description of the universal central extension of g ⊗ R in terms of certain families of polynomials P k,i and Q k,i and describe how the center Ω R /dR decomposes into a direct sum of irreducible representations when the automorphism group is C 2k or D 2k .

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Module structure of the center of the universal central extension of a genus zero Krichever–Novikov algebra

Abstract: We describe how the center of the universal central extension of the genus zero Krichever-Novikov current algebra decomposes as a direct sum of irreducible modules for automorphism group of the coordinate ring of this algebra.

Cited by 2 publications

References 25 publications

On the module structure of the center of hyperelliptic Krichever–Novikov algebras II

On the module structure of the center of hyperelliptic Krichever–Novikov algebras II

On the module structure of the center of hyperelliptic Krichever-Novikov algebras

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