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951.
Adriana Balan 《代数通讯》2013,41(4):1129-1150
If H is a finite dimensional quasi-Hopf algebra and A is a left H-module algebra, we show that there is a Morita context connecting the smash product A#H and the subalgebra of invariants A H . We define also Galois extensions and prove the connection with this Morita context, as in the Hopf case. 相似文献
952.
Xu introduced a family of root-tree-diagram nilpotent Lie algebras of differential operators, in connection with evolution partial differential equations. We generalized his notion to more general oriented tree diagrams. These algebras are natural analogues of the maximal nilpotent Lie subalgebras of finite-dimensional simple Lie algebras. In this article, we use Hodge Laplacian to study the cohomology of these Lie algebras. The “total rank conjecture” and “b 2-conjecture” for the algebras are proved. Moreover, we find the generating functions of the Betti numbers by means of Young tableaux for the Lie algebras associated with certain tree diagrams of single branch point. By these functions and Euler–Poincaré principle, we obtain analogues of the denominator identity for finite-dimensional simple Lie algebras. The result is a natural generalization of the Bott's classical result in the case of special linear Lie algebras. 相似文献
953.
954.
Shuanhong Wang 《代数通讯》2013,41(3):1019-1049
955.
Let A and B be multiplier Hopf algebras, and let R ∈ M(B ? A) be an anti-copairing multiplier, i.e, the inverse of R is a skew-copairing multiplier in the sense of Delvaux [5]. Then one can construct a twisted tensor coproduct multiplier Hopf algebra A ? R B. Using this, we establish the correspondence between the existence of quasitriangular structures in A ? R B and the existence of such structures in the factors A and B. We illustrate our theory with a profusion of examples which cannot be obtained by using classical Hopf algebras. Also, we study the class of minimal quasitriangular multiplier Hopf algebras and show that every minimal quasitriangular Hopf algebra is a quotient of a Drinfel’d double for some algebraic quantum group. 相似文献
956.
We examine a universal algebraic abstraction of the semigroup theoretic concept of “divides:” a divides b in an algebra A if for some n ∈ ω, there is a term t(x, y 1,…, y n ) involving all of the listed variables, and elements c 1,…, c n such that t A (a, c 1,…, c n ) = b. The first order definability of this relation is shown to be a very broad generalisation of some familiar congruence properties, such as definability of principal congruences. The algorithmic problem of deciding when a finitely generated variety has this relation definable is shown to be equivalent to an open problem concerning flat algebras. We also use the relation as a framework for establishing some results concerning the finite axiomatisability of finitely generated varieties. 相似文献
957.
Let X and A be weak Hopf algebras in the sense of Li (1998). As in the case of Hopf algebras (Majid, 1990), a weak bicrossed coproduct X∞ R A is constructed by means of good regular R-matrices of the weak Hopf algebras X and A. Using this, we provide a new framework of obtaining singular solutions of the quantum Yang–Baxter equation by constructing weak quasitriangular structures over X∞ R A when both X and A admit a weak quasitriangular structure. Finally, two explicit examples are given. 相似文献
958.
Adriana Balan 《代数通讯》2013,41(4):1491-1525
In this article, we consider categories of all semimodules over semirings which are p-Schreier varieties, i.e., varieties whose projective algebras are all free. Among other results, we show that over a division semiring R all semimodules are projective iff R is a division ring, prove that categories of all semimodules over proper additively π-regular semirings are not p-Schreier varieties (in particular, this result solves Problem 1 of Katsov [8]), as well as prove that categories of all semimodules over cancellative division semirings are, in contrast, p-Schreier varieties. 相似文献
959.
960.
Tianshui Ma 《代数通讯》2013,41(9):3206-3242
In this article, we first introduce the notion of a bitwistor and discuss conditions under which such bitwistor forms a bialgebra as a generalization of the well-known Radford's biproduct. Then, in order to obtain new quasitriangular bialgebras, we consider a construction called twisted tensor biproduct, which is a special case of bitwistor bialgebra, and give a necessary and sufficient condition for such twisted tensor biproduct to admit quasitriangular structures. 相似文献