| Abstract: |
| Let $B$ be a concealed algebra, denoted by $\mathfrak{im}(B)$ the corresponding (Slowdowy) intersection matrix Lie algebra defined by the matrix of the quadratic form of $B$. Let $C=B\ltimes \text{Ext}^2_B(DB,B)$ be the corresponding cluster-concealed algebra. Based on Ringle`s work on cluster concealed algebras, it is proved that the each real Schur root of $\mathfrak{im}(B)$ can be realized by certain decomposition of some indecomposable $\tau$-rigid $C$-modules when viewed as $B$-module. Moreover, we give a bijection between the positive roots of $\mathfrak{im}(B)$ and the indecomposable $B$-modules. This is a joint work with Changjian Fu and Pin Liu. |
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