Displaying similar documents to “Hall algebras”

Structure of the unit group of the group algebras of non-metabelian groups of order 128

Navamanirajan Abhilash, Elumalai Nandakumar, Rajendra K. Sharma, Gaurav Mittal (2025)

Mathematica Bohemica

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We characterize the unit group for the group algebras of non-metabelian groups of order 128 over the finite fields whose characteristic does not divide the order of the group. Up to isomorphism, there are 2328 groups of order 128 and only 14 of them are non-metabelian. We determine the Wedderburn decomposition of the group algebras of these non-metabelian groups and subsequently characterize their unit groups.

Finite-dimensional Lie subalgebras of algebras with continuous inversion

Daniel Beltiţă, Karl-Hermann Neeb (2008)

Studia Mathematica

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We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion...

Infinitesimal unipotent group schemes of complexity 1

Rolf Farnsteiner, Gerhard Röhrle, Detlef Voigt (2001)

Colloquium Mathematicae

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We classify the uniserial infinitesimal unipotent commutative groups of finite representation type over algebraically closed fields. As an application we provide detailed information on the structure of those infinitesimal groups whose distribution algebras have a representation-finite principal block.

On free subgroups of units in quaternion algebras II

Jan Krempa (2003)

Colloquium Mathematicae

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Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.

Isometries between groups of invertible elements in C*-algebras

Osamu Hatori, Keiichi Watanabe (2012)

Studia Mathematica

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We describe all surjective isometries between open subgroups of the groups of invertible elements in unital C*-algebras. As a consequence the two C*-algebras are Jordan *-isomorphic if and only if the groups of invertible elements in those C*-algebras are isometric as metric spaces.

Problems in the theory of quantum groups

Shuzhou Wang (1997)

Banach Center Publications

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This is a collection of open problems in the theory of quantum groups. Emphasis is given to problems in the analytic aspects of the subject.