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
Consider the canonical isomorphism between the positive part U+ of the quantum group Uq(g) and the Hall algebra H(Λ),where the semisimple Lie algebra g and the finite-dimensional hereditary algebra Λ share a Dynkin ...Consider the canonical isomorphism between the positive part U+ of the quantum group Uq(g) and the Hall algebra H(Λ),where the semisimple Lie algebra g and the finite-dimensional hereditary algebra Λ share a Dynkin diagram.Chen and Xiao have given two algorithms to decompose the root vectors into linear combinations of monomials of Chevalley generators of U+,respectively induced by the braid group action on the exceptional sequences of Λ-modules and the structure of the Auslander-Reiten quiver of Λ.In this paper,we obtain the corresponding algorithms for the derived Hall algebra DH(Λ),which was introduced by Toen.We show that both algorithms are applicable to the lattice algebra and Heisenberg double in the sense of Kapranov.All the new recursive formulae have the same flavor with the quantum Serre relations.展开更多
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.
基金supported by National Natural Science Foundation of China(Grant No.10631010)National Key Basic Research Project of China (Grant No.2006CB805905)
文摘Consider the canonical isomorphism between the positive part U+ of the quantum group Uq(g) and the Hall algebra H(Λ),where the semisimple Lie algebra g and the finite-dimensional hereditary algebra Λ share a Dynkin diagram.Chen and Xiao have given two algorithms to decompose the root vectors into linear combinations of monomials of Chevalley generators of U+,respectively induced by the braid group action on the exceptional sequences of Λ-modules and the structure of the Auslander-Reiten quiver of Λ.In this paper,we obtain the corresponding algorithms for the derived Hall algebra DH(Λ),which was introduced by Toen.We show that both algorithms are applicable to the lattice algebra and Heisenberg double in the sense of Kapranov.All the new recursive formulae have the same flavor with the quantum Serre relations.
