The considerations of the first part culminate in Theorem 1.6 proving isomorphy of the Hopf algebra of representative functions on the real (or complex) Lie algebra L with the Hopf algebra of representative functions on the universal analytic group G corresponding to L. While the interesting part...
Lie余代数(Lie coalgebra) 结构是一个线性映射d:E→E∧E, 满足对偶的 Jacobi 法则. 与g↦Ug相对偶, 由 Lie 余代数E可构造 Hopf 代数Uc(E). Hopf 代数的对偶 设H为 Hopf 代数,H^*=\operatorname{Hom}(H,\mathbb{C})是其作为向量空间的对偶. 回忆 Hopf 代数有以下的结构. ...
At the end, we compute the Hopf cyclic cohomology of the associated Hopf algebra with coefficients in the aforementioned SAYD module in terms of Lie algebra cohomology of the Lie algebra associated to the matched pair object relative to an appropriate Levi subalgebra with coefficients induced by ...
Hopf algebra in exactly the same manner.These algebraic systems play an important role when studying thestructure of G. Similarly, a k-Hopf algebra structure can be definednaturally on the universal enveloping algebra of a k-Lie algebra.The universal enveloping algebra of the Lie algebra of a...
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a...
Many of these chains can be explicitly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution ...
We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–Birkhoff–Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of...
As an application, we deduce that the graded cohomology of color Lie algebra L is isomorphic to the graded Hochschild cohomology of its universal enveloping algebra U ( L ), solving a question of M. Scheunert.doi:10.1016/j.jalgebra.2005.11.026Xiao-Wu Chen...
The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of coefficients (AYD modules) over a topological Lie algebra and those over its universal enveloping (Hopf) algebra are isomorphic. For topological Hopf algebras, the category of coefficients is ...
另外还有一类日益重要的量子群，双叉积量子群[3]，这是通过可解Lie代数形变得到的。有关量子群的几何...