Ringel-Hall Algebras of Duplicated Tame Hereditary Algebras

Details Ringel-Hall Algebras of Duplicated Tame Hereditary Algebras Ringel-Hall Algebras of Duplicated Tame Hereditary Algebras

2010-01-08

arxiv.org/abs/1001.1188v1

Mathematics

Representation Theory

16 pages

Scientific paper

Let $A$ be a tame hereditary algebra over a finite field $k$ with $q$ elements, and ${\bar{A}}$ be the duplicated algebra of $A$. In this paper, we investigate the structure of Ringel-Hall algebra $\mathscr{H} (\bar{A})$ and of the corresponding composition algebra $\mathscr{C} (\bar{A})$. As an application, we prove the existence of Hall polynomials $g_{XY}^M$ for any $\bar{A}$-modules $M, X$ and $Y$ with $X$ and $Y$ indecomposable if $A$ is a tame quiver $k$-algebra, then we also obtain some Lie subalgebras induced by $\bar{A}$.

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