Displaying similar documents to “On some spaces of linear functionals on the algebras A p ( G ) for locally compact groups”

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

Xiao Chen, Anthony To-Ming Lau, Chi-Keung Ng (2015)

Studia Mathematica

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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...

On unit group of finite semisimple group algebras of non-metabelian groups up to order 72

Gaurav Mittal, Rajendra Kumar Sharma (2021)

Mathematica Bohemica

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We characterize the unit group of semisimple group algebras 𝔽 q G of some non-metabelian groups, where F q is a field with q = p k elements for p prime and a positive integer k . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group ( ( C 3 × C 3 ) ⋊ C 3 ) ⋊ C 2 of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.

Operator Figà-Talamanca-Herz algebras

Volker Runde (2003)

Studia Mathematica

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Let G be a locally compact group. We use the canonical operator space structure on the spaces L p ( G ) for p ∈ [1,∞] introduced by G. Pisier to define operator space analogues O A p ( G ) of the classical Figà-Talamanca-Herz algebras A p ( G ) . If p ∈ (1,∞) is arbitrary, then A p ( G ) ⊂ O A p ( G ) and the inclusion is a contraction; if p = 2, then OA₂(G) ≅ A(G) as Banach spaces, but not necessarily as operator spaces. We show that O A p ( G ) is a completely contractive Banach algebra for each p ∈ (1,∞), and that O A q ( G ) ⊂ O A p ( G ) completely contractively...

Quantised 𝔰𝔩 2 -differential algebras

Andrey Krutov, Pavle Pandžić (2024)

Archivum Mathematicum

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We propose a definition of a quantised 𝔰𝔩 2 -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of  𝔰𝔩 2 are natural examples of such algebras.

Algebras whose groups of units are Lie groups

Helge Glöckner (2002)

Studia Mathematica

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Let A be a locally convex, unital topological algebra whose group of units A × is open and such that inversion ι : A × → A × is continuous. Then inversion is analytic, and thus A × is an analytic Lie group. We show that if A is sequentially complete (or, more generally, Mackey complete), then A × has a locally diffeomorphic exponential function and multiplication is given locally by the Baker-Campbell-Hausdorff series. In contrast, for suitable non-Mackey complete A, the unit group A × is an analytic Lie...

Group algebras whose groups of normalized units have exponent 4

Victor Bovdi, Mohammed Salim (2018)

Czechoslovak Mathematical Journal

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We give a full description of locally finite 2 -groups G such that the normalized group of units of the group algebra F G over a field F of characteristic 2 has exponent 4 .

Dual complementors in topological algebras

Marina Haralampidou (2005)

Banach Center Publications

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We deal with dual complementors on complemented topological (non-normed) algebras and give some characterizations of a dual pair of complementors for some classes of complemented topological algebras. The study of dual complementors shows their deep connection with dual algebras. In particular, we refer to Hausdorff annihilator locally C*-algebras and to proper Hausdorff orthocomplemented locally convex H*-algebras. These algebras admit, by their nature, the same type of dual pair of...

On a translation property of positive definite functions

Lars Omlor, Michael Leinert (2010)

Banach Center Publications

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If G is a locally compact group with a compact invariant neighbourhood of the identity e, the following property (*) holds: For every continuous positive definite function h≥ 0 with compact support there is a constant C h > 0 such that ∫ L x h · g ≤ C h ∫ h g for every continuous positive definite g≥0, where L x is left translation by x. In [L], property (*) was stated, but the above inequality was proved for special h only. That “for one h” implies “for all h” seemed obvious, but turned out not to be obvious at...

On locally S -closed spaces

Takashi Noiri (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si studiano le condizioni sotto cui l’immagine (o l'immagine inversa) di uno spazio localmente S -chiuso sia localmente S -chiuso.

On locally S -closed spaces

Takashi Noiri (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Si studiano le condizioni sotto cui l’immagine (o l'immagine inversa) di uno spazio localmente S -chiuso sia localmente S -chiuso.

Quantized semisimple Lie groups

Rita Fioresi, Robert Yuncken (2024)

Archivum Mathematicum

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The goal of this expository paper is to give a quick introduction to q -deformations of semisimple Lie groups. We discuss principally the rank one examples of 𝒰 q ( 𝔰𝔩 2 ) , 𝒪 ( SU q ( 2 ) ) , 𝒟 ( SL q ( 2 , ℂ ) ) and related algebras. We treat quantized enveloping algebras, representations of 𝒰 q ( 𝔰𝔩 2 ) , generalities on Hopf algebras and quantum groups, * -structures, quantized algebras of functions on q -deformed compact semisimple groups, the Peter-Weyl theorem, * -Hopf algebras associated to complex semisimple Lie groups and the Drinfeld...