You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Multiplier Hopf Algebras
A. Van Daele
Transactions of the American Mathematical Society
Vol. 342, No. 2 (Apr., 1994), pp. 917-932
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2154659
Page Count: 16
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
In this paper we generalize the notion of Hopf algebra. We consider an algebra A, with or without identity, and a homomorphism Δ from A to the multiplier algebra M(A ⊗ A) of A ⊗ A. We impose certain conditions on Δ (such as coassociativity). Then we call the pair (A, Δ) 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 (Δ f)(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.
Transactions of the American Mathematical Society © 1994 American Mathematical Society