The relationships between Koszulity and finite Galois coverings are obtained, which provide a construction of Koszul algebras by finite Galois coverings.
Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated ex...Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated explicitly. And the cyclic homology of∧ can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from i≥1 HH^i（∧） to i≥1 HH^i（∧）.展开更多
We consider the Zn-Galois covering An of the algebra A introduced by F. Xu [Adv. Math., 2008, 219： 1872-1893]. We calculate the dimensions of all Hochschild cohomology groups of An and give the ring structure of the ...We consider the Zn-Galois covering An of the algebra A introduced by F. Xu [Adv. Math., 2008, 219： 1872-1893]. We calculate the dimensions of all Hochschild cohomology groups of An and give the ring structure of the Hochschild cohomology ring modulo nilpotence. As a conclusion, we provide a class of counterexamples to Snashall-Solberg＇s conjecture.展开更多
We introduce splitting coverings to enhance the well known analogy between field extensions and covering spaces. Semi-topological Galois groups are defined for Weier- strass polynomials and a Galois correspondence is ...We introduce splitting coverings to enhance the well known analogy between field extensions and covering spaces. Semi-topological Galois groups are defined for Weier- strass polynomials and a Galois correspondence is proved. Combining results from braid groups, we solve the topological inverse Galois problem. As an application, symmetric and cyclic groups are realized over Q.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10731070)
文摘The relationships between Koszulity and finite Galois coverings are obtained, which provide a construction of Koszul algebras by finite Galois coverings.
基金Supported by National Natrual Science Foundation of China (Grant No.10501010)
文摘Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated explicitly. And the cyclic homology of∧ can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from i≥1 HH^i（∧） to i≥1 HH^i（∧）.
文摘We consider the Zn-Galois covering An of the algebra A introduced by F. Xu [Adv. Math., 2008, 219： 1872-1893]. We calculate the dimensions of all Hochschild cohomology groups of An and give the ring structure of the Hochschild cohomology ring modulo nilpotence. As a conclusion, we provide a class of counterexamples to Snashall-Solberg＇s conjecture.
文摘We introduce splitting coverings to enhance the well known analogy between field extensions and covering spaces. Semi-topological Galois groups are defined for Weier- strass polynomials and a Galois correspondence is proved. Combining results from braid groups, we solve the topological inverse Galois problem. As an application, symmetric and cyclic groups are realized over Q.
