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Frobenius n-group algebras

Biljana Zeković (2002)

Discussiones Mathematicae - General Algebra and Applications

Frobenius algebras play an important role in the representation theory of finite groups. In the present work, we investigate the (quasi) Frobenius property of n-group algebras. Using the (quasi-) Frobenius property of ring, we can obtain some information about constructions of module category over this ring ([2], p. 66-67).

Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems

S. Bezuglyi, K. Medynets (2008)

Colloquium Mathematicae

We consider the full group [φ] and topological full group [[φ]] of a Cantor minimal system (X,φ). We prove that the commutator subgroups D([φ]) and D([[φ]]) are simple and show that the groups D([φ]) and D([[φ]]) completely determine the class of orbit equivalence and flip conjugacy of φ, respectively. These results improve the classification found in [GPS]. As a corollary of the technique used, we establish the fact that φ can be written as a product of three involutions from [φ].

Fully commutative Kazhdan-Lusztig cells

Richard M. Green, Jozsef Losonczy (2001)

Annales de l’institut Fourier

We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the Temperley-Lieb algebra.

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