Associative conformal algebras of linear growth.

DOI10.1006/JABR.2000.8616zbMath1151.17312arXivmath/0005258OpenAlexW4212788909MaRDI QIDQ5936198

Alexander Retakh

Publication date: 10 July 2001

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0005258

zbMATH Keywords

conformal algebras of linear growthconformal identityGelfand-Kirillov dimensionunital associative conformal algebras

Mathematics Subject Classification ID

Growth rate, Gelfand-Kirillov dimension (16P90) Vertex operators; vertex operator algebras and related structures (17B69) Rings of differential operators (associative algebraic aspects) (16S32)

Related Items (18)

Unital associative pseudoalgebras and their representations ⋮ On irreducible algebras of conformal endomorphisms over a linear algebraic group ⋮ On associative conformal algebras of linear growth. II. ⋮ \(\mathcal{O}\)-operators and Nijenhuis operators of associative conformal algebras ⋮ The 𝓞N-structure on bimodules over associative conformal algebras ⋮ On the Hochschild cohomologies of associative conformal algebras with a finite faithful representation ⋮ Gerstenhaber algebra of the Hochschild cohomology of an associative conformal algebra ⋮ On universal conformal envelopes for quadratic Lie conformal algebras ⋮ Universally defined representations of Lie conformal superalgebras ⋮ Conformal derivations of semidirect products of Lie conformal algebras and their conformal modules ⋮ Triviality of the second cohomology group of the conformal algebras $\mathrm {Cend}_n$ and $\mathrm {Cur}_n$ ⋮ Associative conformal algebras with finite faithful representation. ⋮ On finite representations of conformal algebras ⋮ Extending structures for associative conformal algebras ⋮ On antisymmetric infinitesimal conformal bialgebras ⋮ Simple associative conformal algebras of linear growth ⋮ ON THE WEDDERBURN PRINCIPAL THEOREM IN CONFORMAL ALGEBRAS ⋮ On the classification of subalgebras of \(\text{Cend}_N\) and \(\text{gc}_N\).

Cites Work

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• Prime affine algebras of Gelfand-Kirillov dimension one
• Structure theory of finite conformal algebras
• On free conformal and vertex algebras
• Local systems of vertex operators, vertex superalgebras and modules
• Determination of the differentiably simple rings with a minimal ideal
• Differentiably Simple Rings
• Vertex algebras, Kac-Moody algebras, and the Monster
• Affine algebras of Gelfand-Kirillov dimension one are PI
• On the Jacobian conjecture

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