Group-Graded Twisted Calabi--Yau Algebras
Yasmeen S. Baki

TL;DR
This paper extends the concept of twisted Calabi--Yau algebras to arbitrary abelian group gradings, explores their properties under localization, and surveys various concrete examples including Weyl and universal enveloping algebras.
Contribution
It introduces a new definition for G-graded twisted Calabi--Yau algebras for any abelian group G and studies their stability under localization, broadening the class of known examples.
Findings
G-graded twisted Calabi--Yau algebras are characterized by G-graded twisted Calabi--Yau condition.
Localizations at certain elements preserve the twisted Calabi--Yau property.
Numerous examples including Weyl algebras and universal enveloping algebras are classified as G-graded twisted Calabi--Yau.
Abstract
Historically, the study of graded (twisted or otherwise) Calabi--Yau algebras has meant the study of such algebras under an -grading. In this paper, we propose a suitable definition for a twisted -graded Calabi-Yau algebra, for an arbitrary abelian group. Building on the work of Reyes and Rogalski, we show that a -graded algebra is twisted Calabi-Yau if and only if it is -graded twisted Calabi--Yau. In the second half of the paper, we prove that localizations of twisted Calabi--Yau algebras at elements which form both left and right denominator sets remain twisted Calabi--Yau. As such, we obtain a large class of -graded twisted Calabi--Yau algebras arising as localizations of Artin-Schelter regular algebras. Throughout the paper, we survey a number of concrete examples of -graded twisted Calabi--Yau algebras, including the Weyl algebras, families…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry
