We devote to the calculation of Batalin–Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi–Yau generalized Weyl algebras.We first establish a Van den Bergh duality at the level of complex.Then...We devote to the calculation of Batalin–Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi–Yau generalized Weyl algebras.We first establish a Van den Bergh duality at the level of complex.Then based on the results of Solotar et al.,we apply Kowalzig and Krähmer's method to the Hochschild homology of generalized Weyl algebras,and translate the homological information into cohomological one by virtue of the Van den Bergh duality,obtaining the desired Batalin–Vilkovisky algebra structures.Finally,we apply our results to quantum weighted projective lines and Podleśquantum spheres,and the Batalin–Vilkovisky algebra structures for them are described completely.展开更多
Let Ag=k(x,y)/(x^(2),xy+qyx,y^(2))over a field k.We give a clear character-ization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of A_(q)for any q≠O,and the Gerstenhaber algebraic structure o...Let Ag=k(x,y)/(x^(2),xy+qyx,y^(2))over a field k.We give a clear character-ization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of A_(q)for any q≠O,and the Gerstenhaber algebraic structure on Hochschild cohomology of A_(q)for q=0.展开更多
This paper is devoted to study Frobenius Poisson algebras. We introduce pseudo-unimodular Poisson algebras by generalizing unimodular Poisson algebras, and investigate Batalin-Vilkovisky structures on their cohomology...This paper is devoted to study Frobenius Poisson algebras. We introduce pseudo-unimodular Poisson algebras by generalizing unimodular Poisson algebras, and investigate Batalin-Vilkovisky structures on their cohomology algebras. For any Frobenius Poisson algebra, all Eatalin-Vilkovisky opera tors on its Poisson cochain complex are described explicitly. It is proved that there exists a Batalin-Vilkovisky operator on its cohomology algebra which is induced from a Batalin-Vilkovisky operator on the Poisson cochain complex, if and only if the Poisson st rue ture is pseudo-unimodular. The relation bet ween modular derivations of polynomial Poisson algebras and those of their truncated Poisson algebras is also described in some cases.展开更多
We show that the normalized cochain complex of a nonsymmetric cyclic operad with multiplication is a Quesney homotopy BV algebra;as a consequence,the cohomology groups form a Batalin-Vilkovisky algebra,which is a resu...We show that the normalized cochain complex of a nonsymmetric cyclic operad with multiplication is a Quesney homotopy BV algebra;as a consequence,the cohomology groups form a Batalin-Vilkovisky algebra,which is a result due to L.Menichi.We provide ample examples.展开更多
In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We wil...In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-imons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky （BV） formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11301144,11771122,11801141).
文摘We give a complete description of the Batalin-Vilkovisky algebra structure on Hochschild cohomology of the self-injective quadratic monomial algebras.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11971418).
文摘We devote to the calculation of Batalin–Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi–Yau generalized Weyl algebras.We first establish a Van den Bergh duality at the level of complex.Then based on the results of Solotar et al.,we apply Kowalzig and Krähmer's method to the Hochschild homology of generalized Weyl algebras,and translate the homological information into cohomological one by virtue of the Van den Bergh duality,obtaining the desired Batalin–Vilkovisky algebra structures.Finally,we apply our results to quantum weighted projective lines and Podleśquantum spheres,and the Batalin–Vilkovisky algebra structures for them are described completely.
基金supported by NSFC(Nos.11771122,11801141 and 11961007).
文摘Let Ag=k(x,y)/(x^(2),xy+qyx,y^(2))over a field k.We give a clear character-ization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of A_(q)for any q≠O,and the Gerstenhaber algebraic structure on Hochschild cohomology of A_(q)for q=0.
基金the School Foundation of Shanghai Normal University (project SK201712)the National Natural Science Foundation of China (Grant Nos. 11301180, 11771085)the National Natural Science Foundation of China (Grant Nos. 11771085, 11331006).
文摘This paper is devoted to study Frobenius Poisson algebras. We introduce pseudo-unimodular Poisson algebras by generalizing unimodular Poisson algebras, and investigate Batalin-Vilkovisky structures on their cohomology algebras. For any Frobenius Poisson algebra, all Eatalin-Vilkovisky opera tors on its Poisson cochain complex are described explicitly. It is proved that there exists a Batalin-Vilkovisky operator on its cohomology algebra which is induced from a Batalin-Vilkovisky operator on the Poisson cochain complex, if and only if the Poisson st rue ture is pseudo-unimodular. The relation bet ween modular derivations of polynomial Poisson algebras and those of their truncated Poisson algebras is also described in some cases.
文摘We show that the normalized cochain complex of a nonsymmetric cyclic operad with multiplication is a Quesney homotopy BV algebra;as a consequence,the cohomology groups form a Batalin-Vilkovisky algebra,which is a result due to L.Menichi.We provide ample examples.
文摘In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-imons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky （BV） formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.
