On free differentials on associative algebras
A. Borowiec, V. K. Kharchenko, Zbigniew Oziewicz
TL;DR
This paper introduces the concept of free differentials on associative algebras, explores their existence, and constructs optimal calculi for specific cases, providing examples and theoretical insights.
Contribution
It defines free differentials with a uniqueness property, addresses their existence, and constructs optimal calculi for homogeneous cases in associative algebras.
Findings
Defined free differentials with a uniqueness property
Provided explicit construction of optimal calculi for homogeneous cases
Presented examples illustrating the concepts
Abstract
A free differential for an arbitrary associative algebra is defined as a differential with a uniqueness property. The existence problem for such a differential is posed. The notion of optimal calculi for given commutation rules is introduced and an explicit construction of it for a homogenous case is provided. Some examples are presented.
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
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Polynomial and algebraic computation