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

Co- Versus Contravariant Finiteness of Categories of Representations (1407.2300v1)

Published 8 Jul 2014 in math.RT and math.RA

Abstract: This article supplements recent work of the authors. (1) A criterion for failure of covariant finiteness of a full subcategory of $\Lambda\text{-mod}$ is given, where $\Lambda$ is a finite dimensional algebra. The criterion is applied to the category ${\cal P}{\infty}(\Lambda\rm{-mod})$ of all finitely generated $\Lambda$-modules of finite projective dimension, yielding a negative answer to the question whether ${\cal P}{\infty}(\Lambda\rm{-mod})$ is always covariantly finite in $\Lambda\text{-mod}$. Part (2) concerns contravariant finiteness of ${\cal P}{\infty}(\Lambda\rm{-mod})$. An example is given where this condition fails, the failure being, however, curable via a sequence of one-point extensions. In particular, this example demonstrates that curing failure of contravariant finiteness of ${\cal P}{\infty}(\Lambda\rm{-mod})$ usually involves a tradeoff with respect to other desirable qualities of the algebra.

Summary

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