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PROBABILISTICALLY NILPOTENT HOPF ALGEBRAS.
- Source :
-
Transactions of the American Mathematical Society . Jun2016, Vol. 368 Issue 6, p4295-4314. 20p. - Publication Year :
- 2016
-
Abstract
- In this paper we investigate nilpotenct and probabilistically nilpotent Hopf algebras. We define nilpotency via a descending chain of commutators and give a criterion for nilpotency via a family of central invertible elements. These elements can be obtained from a commutator matrix A which depends only on the Grothendieck ring of H. When H is almost cocommutative we introduce a probabilistic method. We prove that every semisimple quasitriangular Hopf algebra is probabilistically nilpotent. In a sense we thereby answer the title of our paper Are we counting or measuring anything? by Yes, we are. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NILPOTENT groups
*FINITE groups
*HOPF algebras
*ALGEBRAIC topology
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 368
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 112685963
- Full Text :
- https://doi.org/10.1090/tran/6462