Gelfand-Kirillov dimension of commutative subalgebras of simple inﬁnite dimensional algebras and their quotient division algebras

Bavula, V. V.

doi:10.1515/crll.2005.2005.582.61

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Cited by 3 publications

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“…the transcendence degree tr.deg K (Frac(C)) ≤ n). It follows from Corollary 3.12, [1], that Ev(∆) ≃ Z r and r ≤ n, where ∆ = {δ 1 , . .…”

Section: By Lemmamentioning

confidence: 98%

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Finite Generation of the Group of Eigenvalues for Sets of Derivations or Automorphisms of Division Algebras

Bavula

2008

Communications in Algebra

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Let D be a division algebra such that D ⊗ D o is a Noetherian algebra, and be a set of derivations or automorphisms of the division algebra D, then the group Ev of common eigenvalues (i.e., weights) is a finitely generated abelian group. Typical examples of D are the quotient division algebra Frac X of the ring of differential operators X on a smooth irreducible affine variety X over a field K of characteristic zero, and the quotient division algebra Frac U of the universal enveloping algebra U of a finite dimensional Lie algebra .

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“…the transcendence degree tr.deg K (Frac(C)) ≤ n). It follows from Corollary 3.12, [1], that Ev(∆) ≃ Z r and r ≤ n, where ∆ = {δ 1 , . .…”

Section: By Lemmamentioning

confidence: 98%

“…A K-derivation δ of an algebra A is called locally finite if, for each a ∈ A, dim K ( i≥0 Kδ i (a)) < ∞. In a view of Corollary 3.12, [1] and Theorem 3.8, the author propose the following conjecture.…”

Section: By Lemmamentioning

confidence: 99%