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Hochschild homology and cohomology of generalized Weyl algebras

Marco A. Farinati, Andrea L. Solotar, Mariano Suárez-Álvarez (2003)

Annales de l’institut Fourier

We compute Hochschild homology and cohomology of a class of generalized Weyl algebras, introduced by V. V. Bavula in St. Petersbourg Math. Journal, 4 (1) (1999), 71-90. Examples of such algebras are the n-th Weyl algebras, 𝒰 ( 𝔰 𝔩 2 ) , primitive quotients of 𝒰 ( 𝔰 𝔩 2 ) , and subalgebras of invariants of these algebras under finite cyclic groups of automorphisms. We answer a question of Bavula–Jordan (Trans. A.M.S., 353 (2) (2001), 769-794) concerning the generators of the group of automorphisms of a generalized Weyl...

Homogeneous approximations and local observer design

Tomas Ménard, Emmanuel Moulay, Wilfrid Perruquetti (2013)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the construction of local observers for nonlinear systems without inputs, satisfying an observability rank condition. The aim of this study is, first, to define an homogeneous approximation that keeps the observability property unchanged at the origin. This approximation is further used in the synthesis of a local observer which is proven to be locally convergent for Lyapunov-stable systems. We compare the performance of the homogeneous approximation observer with the...

Homogeneous polynomials with isomorphic Milnor algebras

Imran Ahmed (2010)

Czechoslovak Mathematical Journal

We recall first Mather's Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. We show that two homogeneous polynomials having isomorphic Milnor algebras are right-equivalent.

Homological dimensions and approximate contractibility for Köthe algebras

Alexei Yu. Pirkovskii (2010)

Banach Center Publications

We give a survey of our recent results on homological properties of Köthe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of Köthe algebras are also presented.

Homological dimensions for endomorphism algebras of Gorenstein projective modules

Aiping Zhang, Xueping Lei (2024)

Czechoslovak Mathematical Journal

Let A be a CM-finite Artin algebra with a Gorenstein-Auslander generator E , M be a Gorenstein projective A -module and B = End A M . We give an upper bound for the finitistic dimension of B in terms of homological data of M . Furthermore, if A is n -Gorenstein for 2 ≤ n < ∞ , then we show the global dimension of B is less than or equal to n plus the B -projective dimension of Hom A ( M , E ) . As an application, the global dimension of End A E is less than or equal to n .

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