Mathematics – Representation Theory
Scientific paper
2009-02-19
Mathematics
Representation Theory
17 pages
Scientific paper
Let $B$ be a representation-finite $\mathbb{C}$-algebra. The $\mathbb{Z}$-Lie algebra $L(B)$ associated with $B$ has been defined by Ch. Riedtmann. If $B$ is representation-directed there is another $\mathbb{Z}$-Lie algebra associated with $B$ defined by C. M. Ringel and denoted by $\CK(B)$. We prove that the Lie algebras $L(B)$ and $\CK(B)$ are isomorphic for any representation-directed $\mathbb{C}$-algebra $B$.
Kasjan Stanisław
Kosakowska Justyna
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