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991.
Mariam Imtiaz 《代数通讯》2013,41(8):3095-3112
Abstract Let R = K[y 1,…,y t ] be an affine domain over a field K and I be a nonzero proper ideal of R. In Sec. 1 of this note, we characterize when (K + I, R) is a Mori pair. In Sec. 2 of this note, we prove the following theorem: Let A ? B be domains such that C/Q is Mori for each subring C of B containing A and for any prime ideal Q of C. Then dim A ? 1 ≤ dim B ≤ dim A + 1 and if dim A > 1 or dim B > 1 then dim A = dim B. 相似文献
992.
Glenn Rice 《代数通讯》2013,41(8):3047-3055
Let (R, 𝔪) be a Noetherian local ring and M be a submodule of the free module F = R r with height(I r (M)) > 0. Asymptotic sequences over M will be defined analogous to Rees’ definition of asymptotic sequences over an ideal. It is then shown that all maximal asymptotic sequences over M have the same length. This length gives a bound on the analytic spread of M. Namely, if s is the length of a maximal asymptotic sequence over M then l(M) ≤dim R + rank M ? 1 ? s. Equality holds if R is quasi-unmixed. 相似文献
993.
Naihong Hu 《代数通讯》2013,41(9):3202-3220
This article is the sequel to [11] to study the deformed structures and representations of two-parameter quantum groups U r, s (𝔤) associated to the finite dimensional simple Lie algebras 𝔤. An equivalence of the braided tensor categories 𝒪 r, s and 𝒪 q under the assumption rs ?1 = q 2 is explicitly established. 相似文献
994.
Miriam Cohen 《代数通讯》2013,41(12):4618-4633
We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ?2 where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS 3), which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums. 相似文献
995.
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
996.
Jingcheng Dong 《代数通讯》2013,41(12):4673-4678
Let p, q be prime numbers with p > q 3, and k an algebraically closed field of characteristic 0. In this article, we obtain the structure theorems for semisimple Hopf algebras of dimension pq 3. 相似文献
997.
The quantum doubles of a certain class of rank two pointed Hopf algebras are considered. The socle of the tensor product of two such modules is computed, and formulas similar to the ones in [4] are obtained. Cases when such a tensor product is completely irreducible are also given in the last section. 相似文献
998.
Nils Mahrt 《代数通讯》2013,41(7):2420-2425
For a wild acyclic quiver Q, Kerner introduced the notion of exceptional components for the Auslander–Reiten quiver of Q over an algebraically closed field k. He then defined two invariants for these exceptional components and asked whether these invariants coincide for each exceptional component. He showed that for each exceptional component there is a related hereditary factor algebra B of the path algebra kQ. He then proved that B is tame or representation finite and asked whether the representation finite case does occur, at all. We will answer both of Kerner's questions. 相似文献
999.
Richard Varro 《代数通讯》2013,41(7):2426-2448
We give the identities generating the spaces of degree 4 multilinear identities satisfied by the non commutative 0th-order Bernstein algebras and the non commutative mutation algebras. For it, we use a method reducing the search for multilinear identities to the resolution of linear systems. 相似文献
1000.