arXiv subjects
Publications and source records attributed to Mariano Suárez-Alvarez.
Jake Goodman and Ulrich Krähmer have recently shown that a twisted Calabi-Yau algebra $A$ with modular automorphism $σ$ and dimension $d$ can be "untwisted," in the sense that the Ore extensions $A[X;σ]$ and $A[X^{\pm1};σ]$ are Calabi-Yau algebras of dimension $d+1$. In this note we show that this in fact extends more generally to the case where we start with an algebra with van den Bergh duality.
We classify up to isomorphism the quantum generalized Weyl algebras and determine their automorphism groups in all cases in a uniform way, including those where the parameter q is a root of unity, thereby completing the results obtained by [Bavula, V. V.; Jordan, D. A. Isomorphism problems and groups of automorphisms for generalized Weyl algebras. Trans. Amer. Math. Soc. 353 (2001), no. 2, 769-794] and [Richard, L.; Solotar, A. Isomorphisms between quantum generalized Weyl algebras. J. Algebra Appl. 5 (2006), no. 3, 271-285]
We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of 'quantum' type in all but a few exceptional cases.
We consider the change-of-rings spectral sequence as it applies to Hochschild cohomology, obtaining a description of the differentials on the first page which relates it to the multiplicative stucture on cohomology. Using this information, we are able to completely describe the cohomology structure of monogenic algebras as well as some information on the structure of the cohomology in more general situations. We also show how to use the spectral sequence to reprove and generalize results of M. Auslander et. al. about homological epimorphisms. We derive from this a rather general version of the long exact sequence due to D. Happel for a one-point (co)-extension of a finite dimensional algebra and show how it can be put to use in concrete examples.