Multiplier Hopf algebras
Multiplier Hopf algebras
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DOI：
10.1090/s0002-9947-1994-1220906-5
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发表时间：
1994-02
影响因子：
1.3
通讯作者：
A. V. Daele
中科院分区：
文献类型：
--
作者：
A. V. Daele
本文推广了Hopf代数的概念。我们考虑有或没有单位元的代数A，以及从A到A的乘子代数M(A®A)的同态A。我们对A施加某些条件(例如共结合性)。然后我们称{A，A)为乘子Hopf代数。一个令人振奋的例子是A是群G上有限支承复函数的代数，其中(Af)(S，t)=f(St)且有S，t GB G和f EURO A。我们证明了正极和对极的存在。如果A有一个恒等式，我们就有一个常见的Hopf代数。我们还考虑了A是*-代数的情况。然后，我们证明了对偶空间的(足够大的)子空间也可以变成*-代数。
In this paper we generalize the notion of Hopf algebra. We consider an algebra A , with or without identity, and a homomorphism A from A to the multiplier algebra M(A ® A) of A ® A . We impose certain conditions on A (such as coassociativity). Then we call the pair {A, A) a multiplier Hopf algebra. The motivating example is the case where A is the algebra of complex, finitely supported functions on a group G and where (Af)(s, t) = f(st) with s, t £ G and f € A . We prove the existence of a counit and an antipode. If A has an identity, we have a usual Hopf algebra. We also consider the case where A is a *-algebra. Then we show that (a large enough) subspace of the dual space can also be made into a *-algebra.