Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Algebra endomorphisms and Derivations of Some Localized Down-Up Algebras (1403.6536v1)

Published 26 Mar 2014 in math.RA

Abstract: We study algebra endomorphisms and derivations of some localized down-up algebras $\A$. First, we determine all the algebra endomorphisms of $\A$ under some conditions on $r$ and $s$. We show that each algebra endomorphism of $\A$ is an algebra automorphism if $r{m}s{n}=1$ implies $m=n=0$. When $r=s{-1}=q$ is not a root of unity, we give a criterion for an algebra endomorphism of $\A$ to be an algebra automorphism. In either case, we are able to determine the algebra automorphism group for $\A$. We also show that each surjective algebra endomorphism of the down-up algebra $A(r+s, -rs)$ is an algebra automorphism in either case. Second, we determine all the derivations of $\A$ and calculate its first degree Hochschild cohomology group.

Summary

We haven't generated a summary for this paper yet.