publication . Preprint . Article . Other literature type . 2012

Graded associative conformal algebras of finite type

Kolesnikov, Pavel;
Open Access English
  • Published: 26 Aug 2012
Abstract
In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\Gamma $ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\simeq \Gamma $. A classification of simple and semisimple graded associative conformal algebras of finite type is obtained.
Subjects
arXiv: Mathematics::Rings and Algebras
free text keywords: Mathematics - Quantum Algebra, Mathematics - Rings and Algebras, General Mathematics, Algebra, Division algebra, Quantum group, Mathematics, Differential graded algebra, Algebra representation, Universal enveloping algebra, Topology, Hopf algebra, Subalgebra, Lie conformal algebra

v ∈ U. Here aγ ∈ Hom(Vγ , Vαγ ). Denote aγk by ak, k = 1, . . . , p. Note that if γ ∈ Γk, αγ ∈ Γm then emaek ∈ Aα, so P aγ ∈ Aα for every k = 1, . . . , p. γ∈Γk If αγk ∈/ Γ0 then Wα,γ = {b ∈ Hom(Vγ , Vαγ ) | ∃a ∈ Aα : aγ = b} 6= 0 for every γ ∈ Γk. Since Wα,γ is a (End Vαγ )-(End Vγ )-bimodule embedded into Hom(Vγ , Vαγ ), we have Wα,γ = Hom(Vγ , Vαγ ). Given γ ∈ Γk, α ∈ Γ, αΓk = Γm, the map σα,γ : ak 7→ aγ, a ∈ Aα, is a linear bijection between Hom(Vγk , Vαγk ) and Hom(Vγ , Vαγ ). Assume σα,γk = id and σe,γ (x) = ιγ xιγ−1, since we have already established the structure of Ae. Suppose a = P akσα,γ ∈ Aα, b = P ιβbmιβ−1Tβ ∈ Ae, and consider γ∈Γk β∈Γm

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publication . Preprint . Article . Other literature type . 2012

Graded associative conformal algebras of finite type

Kolesnikov, Pavel;