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71.
72.
Leonid Krop 《代数通讯》2013,41(12):4719-4732
We give definition of the second indicator for any finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0 with the square of antipode an inner automorphism. We derive a closed formula for the trace of the antipode on endomorphism algebras of simple self-dual modules of nilpotent type liftings of quantum linear spaces and compute the value of their second indicators. Uniqueness of indicators is examined. 相似文献
73.
Anders O. F. Hendrickson 《代数通讯》2013,41(12):4420-4438
Diaconis and Isaacs have defined the supercharacter theories of a finite group to be certain approximations to the ordinary character theory of the group [7]. We make explicit the connection between supercharacter theories and Schur rings, and we provide supercharacter theory constructions which correspond to Schur ring products of Leung and Man [12], Hirasaka and Muzychuk [10], and Tamaschke [20]. 相似文献
74.
75.
Brent Kerby 《代数通讯》2013,41(12):5087-5103
In 1993, Muzychuk [23] showed that the rational Schur rings over a cyclic group Z n are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Z n . This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G in a natural way. Our main result is that any finite group may be represented as the (algebraic) automorphism group of such a rational Schur ring over an abelian p-group, for any odd prime p. In contrast, over a cyclic group the automorphism group of any Schur ring is abelian. We also prove a converse to the well-known result of Muzychuk [24] that two Schur rings over a cyclic group are isomorphic if and only if they coincide; namely, we show that over a group which is not cyclic, there always exist distinct isomorphic Schur rings. 相似文献
76.
A finite group G is called a Schur group, if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. Recently, the authors have completely identified the cyclic Schur groups. In this article, it is shown that any abelian Schur group belongs to one of several explicitly given families only. In particular, any noncyclic abelian Schur group of odd order is isomorphic to ?3 × ?3 k or ?3 × ?3 × ? p where k ≥ 1 and p is a prime. In addition, we prove that ?2 × ?2 × ? p is a Schur group for every prime p. 相似文献
77.
通过判断相关函数的Schur凸性、Schur几何凸性和Schur调和凸性,证明并推广了一类条件不等式,并据此建立了某些单形不等式. 相似文献
78.
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80.
《代数通讯》2013,41(9):2921-2940
ABSTRACT An equivalent version of the Generalized Nakayama Conjecture states that any projective almost complete tilting module admits a finite number of non-isomorphic indecomposable complements. Motivated by this connection, we investigate the number of possible complements of projective almost complete tilting modules for some particular classes of Artin algebras, namely monomial algebras and algebras with exactly two simple modules. 相似文献