Filter dimension of algebras and modules, a simplicity criterion of generalized weyl algebras

DOI10.1080/00927879608825683zbMath0855.16005OpenAlexW2103212284MaRDI QIDQ4887962

Vladimir V. Bavula

Publication date: 27 January 1997

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

Full work available at URL: https://doi.org/10.1080/00927879608825683

zbMATH Keywords

growthfinitely generated modulesmultiplicityBernstein inequalityfiltrationsglobal dimensionKrull dimensionGelfand-Kirillov dimensiongeneralized Weyl algebrasassociated graded algebrasholonomic modulesfilter dimensionsimple affine algebrasalmost commutative algebrassimplicity criterion

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Growth rate, Gelfand-Kirillov dimension (16P90) Universal enveloping (super)algebras (17B35) Rings of differential operators (associative algebraic aspects) (16S32) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Homological dimension in associative algebras (16E10) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (20)

The quantum Euclidean algebra and its prime spectrum ⋮ A Bernstein-Gabber-Joseph theorem for affine algebras ⋮ Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras. ⋮ Noncommutative fiber products and lattice models ⋮ PRIME SPECTRA OF AMBISKEW POLYNOMIAL RINGS ⋮ Classification of simple \(\mathfrak{q}_2\)-supermodules ⋮ Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras ⋮ Quiver generalized Weyl algebras, skew category algebras and diskew polynomial rings ⋮ Simple ambiskew polynomial rings. ⋮ The prime spectrum of the algebra \(\mathbb{K}_q[X,Y \rtimes U_q(\mathfrak{sl}_2)\) and a classification of simple weight modules] ⋮ Fixed rings of quantum generalized Weyl algebras ⋮ Generalized Weyl algebras and diskew polynomial rings ⋮ Simple holonomic modules over the second Weyl algebra \(A_2\) ⋮ The global dimension of the generalized Weyl algebras 𝑆⁻¹𝐾[𝐻,𝐶[𝑋,𝑌;𝜎,𝑎]] ⋮ Dimension, multiplicity, holonomic modules, and an analogue of the inequality of Bernstein for rings of differential operators in prime characteristic ⋮ Filter Dimension ⋮ Krull, Gelfand-Kirillov, and filter dimensions of simple affine algebras ⋮ Morita invariance of the filter dimension and of the inequality of Bernstein. ⋮ On projective modules over quantum polynomials ⋮ Holonomic modules for rings of invariant differential operators

Cites Work

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• Finite dimensionality of \(\text{Ext}^ n\)'s and \(\text{Tor}_ n\)'s of simple modules over one class of algebras
• The spectrum of the algebra of skew differential operators and the irreducible representations of the quantum Heisenberg algebra
• A generalization of Quillen's lemma and its application to the Weyl algebras
• Noncommutative deformations of type-\(A\) Kleinian singularities
• Primitivity in skew Laurent polynomial rings and related rings
• Tensor homological minimal algebras, global dimension of the tensor product of algebras and of generalized Weyl algebras
• Structure of representations generated by vectors of highest weight
• Simple D[X, Y; ?,a-modules]
• On completions of non-commutative noetherian rings
• A Class of Algebras Similar to the Enveloping Algebra of sl(2)
• Homological properties of the enveloping algebra U(Sl₂)
• Each Schurian algebra is tensor-simple

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