In this paper, the group action of a local wild Bocs'rep. category is introduced. And, it computed the parametric numbers U(n) and P(n) of the rep. category mod n(A) and ind n(t) in case n=1,2 with geometric met...In this paper, the group action of a local wild Bocs'rep. category is introduced. And, it computed the parametric numbers U(n) and P(n) of the rep. category mod n(A) and ind n(t) in case n=1,2 with geometric method.展开更多
We first give an alternative proof of the well-known Drozd's wild Theorem,which lowers down the dimension 43 to 20. Then we list more minimally wild bocses and discuss the possible differentials of the first arrow...We first give an alternative proof of the well-known Drozd's wild Theorem,which lowers down the dimension 43 to 20. Then we list more minimally wild bocses and discuss the possible differentials of the first arrow of a tame bocs, which is useful for reductions of bocses.展开更多
Bocs, which is the abbreviated form of bimodule over a categary with coalgebra structure, was introduced by Kleiner and Rojter in 1975 and developed by Drozd in 1979, then formulated by Crawley-Boevey in 1988. Let k b...Bocs, which is the abbreviated form of bimodule over a categary with coalgebra structure, was introduced by Kleiner and Rojter in 1975 and developed by Drozd in 1979, then formulated by Crawley-Boevey in 1988. Let k be an algebraically closed field, A a finitely dimensional k-algebra. Then there exists a bocs B over k associated to A. From this relation Drozd proved one of the most important theorems in representation theory of algebra, namely, a finitely dimensional k-algebra is either of representation tame type or of representation wild type,展开更多
The bocs corresponding to each hereditary algebra of representation tame type is shown. And the minimal bocs obtained from it is given with only irreducible maps for each dimension d. The minimal bocs (after deleting ...The bocs corresponding to each hereditary algebra of representation tame type is shown. And the minimal bocs obtained from it is given with only irreducible maps for each dimension d. The minimal bocs (after deleting finitely many vertices) coincides with a full subquiver of the AR-quiver of hereditary algebra, in which the indecomposable modules M have the property dim (top M)<d.展开更多
The bocs corresponding to Kronecker algebra is shown and the corresponding minimal bocs with only irreducible maps Tor each dimension d is also given.The minimal bocs (after deleting two vertices) coincides with a ful...The bocs corresponding to Kronecker algebra is shown and the corresponding minimal bocs with only irreducible maps Tor each dimension d is also given.The minimal bocs (after deleting two vertices) coincides with a full subquiver of the AR-quiver of Kronecker algebra,in which the indecomposable modules M have the property dim(top M)<d.展开更多
文摘In this paper, the group action of a local wild Bocs'rep. category is introduced. And, it computed the parametric numbers U(n) and P(n) of the rep. category mod n(A) and ind n(t) in case n=1,2 with geometric method.
文摘We first give an alternative proof of the well-known Drozd's wild Theorem,which lowers down the dimension 43 to 20. Then we list more minimally wild bocses and discuss the possible differentials of the first arrow of a tame bocs, which is useful for reductions of bocses.
文摘Bocs, which is the abbreviated form of bimodule over a categary with coalgebra structure, was introduced by Kleiner and Rojter in 1975 and developed by Drozd in 1979, then formulated by Crawley-Boevey in 1988. Let k be an algebraically closed field, A a finitely dimensional k-algebra. Then there exists a bocs B over k associated to A. From this relation Drozd proved one of the most important theorems in representation theory of algebra, namely, a finitely dimensional k-algebra is either of representation tame type or of representation wild type,
文摘The bocs corresponding to each hereditary algebra of representation tame type is shown. And the minimal bocs obtained from it is given with only irreducible maps for each dimension d. The minimal bocs (after deleting finitely many vertices) coincides with a full subquiver of the AR-quiver of hereditary algebra, in which the indecomposable modules M have the property dim (top M)<d.
基金Project supported by the National Natural Science Foundation of China and the State Education Commission.
文摘The bocs corresponding to Kronecker algebra is shown and the corresponding minimal bocs with only irreducible maps Tor each dimension d is also given.The minimal bocs (after deleting two vertices) coincides with a full subquiver of the AR-quiver of Kronecker algebra,in which the indecomposable modules M have the property dim(top M)<d.
