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Relative Reduction and Buchberger’s Algorithm in Filtered Free Modules

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1 Published in 2017 at "Mathematics in Computer Science"

DOI: 10.1007/s11786-017-0317-1

Abstract: In this paper we develop a relative Gröbner basis method for a wide class of filtered modules. Our general setting covers the cases of modules over rings of differential, difference, inversive difference and difference–differential operators,… read more here.

Keywords: algorithm; weyl algebras; free modules; filtered free ... See more keywords

The noncommutative schemes of generalized Weyl algebras

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0 Published in 2018 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2018.04.004

Abstract: Abstract The first Weyl algebra over k , A 1 = k 〈 x , y 〉 / ( x y − y x − 1 ) admits a natural Z -grading by letting deg… read more here.

Keywords: noncommutative schemes; schemes generalized; generalized weyl; weyl algebras ... See more keywords

Classification of twisted generalized Weyl algebras over polynomial rings

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0 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2019.10.045

Abstract: Abstract Let R be a polynomial ring in m variables over a field of characteristic zero. We classify all rank n twisted generalized Weyl algebras over R, up to Z n -graded isomorphisms, in terms… read more here.

Keywords: twisted generalized; classification twisted; weyl algebras; generalized weyl ... See more keywords

Fixed rings of quantum generalized Weyl algebras

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0 Published in 2019 at "Communications in Algebra"

DOI: 10.1080/00927872.2020.1755302

Abstract: Abstract Generalized Weyl algebras (GWAs) appear in diverse areas of mathematics including mathematical physics, noncommutative algebra, and representation theory. We study the invariants of quantum GWAs under finite order automorphisms. We extend a theorem of… read more here.

Keywords: generalized weyl; fixed rings; rings quantum; weyl algebras ... See more keywords

Weyl ????-algebras and the Swiss cheese operad

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1 Published in 2020 at "Forum Mathematicum"

DOI: 10.1515/forum-2020-0158

Abstract: Abstract We apply Weyl ????-algebras to prove formality theorems for higher Hochschild cohomology. We present two approaches: via propagators and via the factorization complex. It is shown that the second approach is equivalent to the… read more here.

Keywords: swiss cheese; algebras swiss; weyl algebras; cheese operad ... See more keywords