Graded associative conformal algebras of finite type

Preprint English OPEN
Kolesnikov, Pavel;
(2011)
  • Related identifiers: doi: 10.1007/s10468-012-9368-9
  • Subject: Mathematics - Rings and Algebras | Mathematics - Quantum Algebra
    arxiv: Mathematics::Rings and Algebras
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 grad... View more
  • References (12)
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    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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