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. ...
Journal of AlgebraP. B. Chen and T. S. Wu, Hopf algebras, Lie algebras, and analytic groups, J. Algebra 181(1996),1-15. 2] G. Hochschild and G. D. Mostow, On the algebra of representative functions of an analytic group, Amer. J. Math. 83(1961), 111-136. 3] G. Hochschild ...
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 ...
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 asemi-simple algebraic group turns out to be (in a sense) the dual oftheHopf algebra defined above. These constitute ...
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...
It is well known that every ordinary Lie algebra g admits a universal enveloping algebra U(g), which is a Hopf algebra. We are thus led to the following natural questions: does there exist a universal enveloping algebra for L/A[−1] in Db(A) and, if so, is it a Hopf algebra obj...
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...
HOPF ALGEBRAS 5 For example, if A is any associative k-algebra then A is a Lie algebra if we de?ne [a, b] = ab ? ba for all a, b ∈ A. In particular, when A = Mn (k), we write this as gl(n, k). The universal enveloping algebra of the Lie algebra g is the factor ...
tion5givesanexplicitdescriptionoftheLiealgebraofprimitiveelements ofthedualHopfalgebraandgivesacriterionwhenthisistheassociated Liealgebraofapre-Liealgebra.Section6interpretsthefamilyofcoprod- uctsintermsofdeformationtheory.Finally,Section7sketchesthemore generalframeworkofHopfoperadsandliststheresultsobtainedwhen ...
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 ...