Let F be an algebraically closed field, be a quiver of type An. In this paper we prove that the endomorphism algebras of exceptional sequences over F are sums of finitely many tilted algebras of type Am where m n b...Let F be an algebraically closed field, be a quiver of type An. In this paper we prove that the endomorphism algebras of exceptional sequences over F are sums of finitely many tilted algebras of type Am where m n by using perpendicular categories, and thus the endomorphism algebras of exceptional sequences of type An are representation-finite.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 algebraΛshare a Dynkin diag...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 algebraΛshare 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 ofΛ-modules and the structure of the Auslander-Reiten quiver ofΛ.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
In this paper, let A be a finite dimensional associative algebra over an algebraically closed field h, modA be the category of finite dimensional left A-module and X1,X2,... ,X2, in modA be a complete exceptional sequ...In this paper, let A be a finite dimensional associative algebra over an algebraically closed field h, modA be the category of finite dimensional left A-module and X1,X2,... ,X2, in modA be a complete exceptional sequence, and let E be the endomorphism algebra of X1, X2,..., Xn. We study the global dimension of E, and calculate the Hochschild cohomology and homology groups of E.展开更多
基金Supported by Chinese Postdoctorate FundBeijing Youth Fund
文摘Let F be an algebraically closed field, be a quiver of type An. In this paper we prove that the endomorphism algebras of exceptional sequences over F are sums of finitely many tilted algebras of type Am where m n by using perpendicular categories, and thus the endomorphism algebras of exceptional sequences of type An are representation-finite.
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 algebraΛshare 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 ofΛ-modules and the structure of the Auslander-Reiten quiver ofΛ.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.
基金the National Natural Science Foundation of China （No. 10371036 10671061）+2 种基金 the Natural Science Foundation of Beijing （1042001） the Fund of Beijing Education Committee （No. KM200610005024） Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality and the Fundamental reseaxch Fund of Beijing University of Technology.
文摘In this paper, let A be a finite dimensional associative algebra over an algebraically closed field h, modA be the category of finite dimensional left A-module and X1,X2,... ,X2, in modA be a complete exceptional sequence, and let E be the endomorphism algebra of X1, X2,..., Xn. We study the global dimension of E, and calculate the Hochschild cohomology and homology groups of E.
