Non commutative truncated polynomial extensions
Jorge A. Guccione, Juan J. Guccione, Christian Valqui

TL;DR
This paper introduces non-commutative truncated polynomial extensions of an algebra A, classifies one family completely, and links obstructions in constructing upper triangular extensions to Hochschild homology.
Contribution
It defines a new concept of non-commutative truncated polynomial extensions and provides a complete classification for one family, connecting obstructions to Hochschild homology.
Findings
Complete classification of the first family of extensions.
Obstructions to constructing upper triangular extensions relate to Hochschild homology.
Introduces a new framework for non-commutative polynomial extensions.
Abstract
We introduce the notion of non commutative truncated polynomial extension of an algebra A. We study two families of these extensions. For the first one we obtain a complete classification and for the second one, which we call upper triangular, we find that the obstructions to inductively construct them, lie in the Hochschild homology of A, with coefficients in a suitable A-bimodule.
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 · Homotopy and Cohomology in Algebraic Topology
