A property for locally convex *-algebras related to property (T) and character amenability

• Autorzy: Xiao Chen , Anthony To-Ming Lau , Chi-Keung Ng
• Języki publikacji: EN

Abstrakty

EN

For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let $C_{c}(G)$ be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that $(C_{c}(G),ε_{G})$ has property (FH) if and only if G has property (T). On the other hand, many Banach algebras equipped with canonical characters have property (FH) (e.g., those defined by a nice locally compact quantum group). Furthermore, through our studies on both property (FH) and character amenablility, we obtain characterizations of property (T), amenability and compactness of G in terms of the vanishing of one-sided cohomology of certain topological algebras, as well as in terms of fixed point properties. These three sets of characterizations can be regarded as analogues of one another. Moreover, we show that G is compact if and only if the normed algebra ${f ∈ C_{c}(G): ∫_{G} f(t)dt =0}$ (under $||·||_{L¹(G)}$) admits a bounded approximate identity with the supports of all its elements being contained in a common compact set.

Kategorie tematyczne

• 43A07: Means on groups, semigroups, etc.; amenable groups
• 46H15: Representations of topological algebras
• 46K10: Representations of topological algebras with involution
• 22D20: Representations of group algebras
• 22D15: Group algebras of locally compact groups
• 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
• 22D10: Unitary representations of locally compact groups
• 22D12: Other representations of locally compact groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 227
• Numer: 3
• Strony: 259-286

Daty

wydano

2015

Twórcy

autor

Xiao Chen

• Chern Institute of Mathematics, Nankai University, Tianjin 300071, China

autor

Anthony To-Ming Lau

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G-2G1

autor

Chi-Keung Ng

• Chern Institute of Mathematics, Nankai University, Tianjin 300071, China

Identyfikatory

DOI

10.4064/sm227-3-5