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Hopf Algebras of Dimension 14
Author(s) -
Beattie M.,
Dăscălescu S.
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004927
Subject(s) - mathematics , hopf algebra , dimension (graph theory) , representation theory of hopf algebras , algebraically closed field , quasitriangular hopf algebra , algebra over a field , pure mathematics , division algebra , group algebra , group (periodic table) , filtered algebra , cellular algebra , algebra representation , physics , quantum mechanics
Let H be a finite dimensional non‐semisimple Hopf algebra over an algebraically closed field k of characteristic 0. If H has no nontrivial skew‐primitive elements, some bounds are found for the dimension of H 1 , the second term in the coradical filtration of H . Using these results, it is shown that every Hopf algebra of dimension 14 is semisimple and thus isomorphic to a group algebra or the dual of a group algebra. Also a Hopf algebra of dimension pq where p and q are odd primes with p < q ⩽ 1 + 3 p and q ⩽ 13 is semisimple and thus a group algebra or the dual of a group algebra. Some partial results in the classification problem for dimension 16 are also given.