Extension algebras of standard modules

Details Extension algebras of standard modules Extension algebras of standard modules

2011-10-29

arxiv.org/abs/1110.6502v3

Mathematics

Representation Theory

The final version accepted by Comm. Algebra

Scientific paper

Let $A$ be a finite dimensional $k$-algebra standardly stratified for a partial order $\leqslant$ and $\Delta$ be the direct sum of all standard modules. In this paper we study the extension algebra $E= \text{Ext}_A^{\ast} (\Delta, \Delta)$ of standard modules, characterize the stratification property of $E$ for $\leqslant$ and $\leqslant ^{op}$, and obtain a sufficient condition for $E$ to be a generalized Koszul algebra (in a sense which we define).

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