arXiv math/06084252006-08-16math.RAmath.RT

Some remarks on localization in coalgebras

Gabriel Navarro

备注：: 23 pages

英文摘要：

We analyze the geometry of the Ext-quiver of a coalgebra $C$ in order to study the behavior of simple and injective $C$-comodules under the action of the functors associated to a localizing subcategory of the category of $C$-comodules.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Localization in tame and wild coalgebras

We apply the theory of localization for tame and wild coalgebras in order to prove the following theorem: "Let Q be an acyclic quiver. Then any tame admissible subcoalgebra of KQ is the path coalgebra of a quiver with relations".

2007-01-12math.RAmath.RT

Localization in coalgebras. Applications to finiteness conditions

The injective right comodules appearing in the minimal injective resolution of a finite-dimensional comodule need not to be of finite dimension or even quasi-finite. The obstruction here is that factor comodules of quasi-finite comodules are not in general quasi-finite. This note is mainly devoted to the study of coalgebras for which the class of all quasi-finite right comodules is closed under factor comodules. A major tool here is the local study, in the sense of abstract localization, of the comodules which have all their factors quasi-finite.

2004-03-15math.RAmath.RT

The valued Gabriel quiver of a wedge product and semiprime coalgebras

We make a first approach to the representation theory of the wedge product of coalgebras by means of the description of its valued Gabriel quiver. Then we define semiprime coalgebras and study its category of comodules by the use of localization techniques. In particular, we prove that, whether its Gabriel quiver is locally finite, any monomial semiprime fc-tame coalgebra is string. We also prove a weaker version of Eisenbud-Griffith theorem, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.

2010-10-21math.RAmath.RT

The Coalgebra Automorphism Group of Hopf Algebra $k_q[x, x^{-1}, y]$

Let $k_q[x, x^{-1}, y]$ be the localization of the quantum plane $k_q[x, y]$ over a field $k$, where $0\neq q\in k$. Then $k_q[x, x^{-1}, y]$ is a graded Hopf algebra, which can be regarded as the non-negative part of the quantum enveloping algebra $U_q({\mathfrak sl}_2)$. Under the assumption that $q$ is not a root of unity, we investigate the coalgebra automorphism group of $k_q[x, x^{-1}, y]$. We describe the structures of the graded coalgebra automorphism group and the coalgebra automorphism group of $k_q[x, x^{-1}, y]$, respectively.

2012-07-21math.RA