منابع مشابه
On semisimple Hopf algebras of low dimension
We announce recent progress on the question about the semisolvability of semisimple Hopf algebras of dimension < 60. 2000 AMS Subject Classification: 16W30
متن کاملOn the Semisolvability of Semisimple Hopf Algebras of Low Dimension
We prove that every semisimple Hopf algebra of dimension less than 60 over an algebraically closed field k of characteristic zero is either upper or lower semisolvable up to a cocycle twist. Received by the editor September 2006. 1991 Mathematics Subject Classification. Primary 16W30; Secondary 17B37.
متن کاملFURTHER RESULTS ON SEMISIMPLE HOPF ALGEBRAS OF DIMENSION pq
Let p, q be distinct prime numbers, and k an algebraically closed field of characteristic 0. Under certain restrictions on p, q, we discuss the structure of semisimple Hopf algebras of dimension pq. As an application, we obtain the structure theorems for semisimple Hopf algebras of dimension 9q over k. As a byproduct, we also prove that odd-dimensional semisimple Hopf algebras of dimension less...
متن کاملNormal Hopf Subalgebras of Semisimple Hopf Algebras
In this note the notion of kernel of a representation of a semisimple Hopf algebra is introduced. Similar properties to the kernel of a group representation are proved in some special cases. In particular, every normal Hopf subalgebra of a semisimple Hopf algebra H is the kernel of a representation of H
متن کاملHopf Algebras of Dimension
Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integers n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd primes p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some pro...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.06.007