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The Hadamard matrices of order 44 possessing automorphisms of order 7 are classified. The number of their equivalence classes is 384. The order of their full automorphism group is calculated. These Hadamard matrices yield 1683 nonisomorphic 3-(44,22,10) designs, 57932 nonisomorphic 2-(43,21,10) designs, and two inequivalent extremal binary self-dual doubly even codes of length 88 (one of them being new).  相似文献   

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K. A. Hardie and K. H. Kamps investigated the track homotopy categoryH B over a fixed spaceB ([1]). They have introduced two pairs of adjoint functors:P B N B andm * m *, whereP B :H B H B , andm *:H A H B for a fixed mapm:A→B. We have introduced a split fibration of categoriesL:H b H B and provedL J, J L in [2]. This paper first extendsP B N B to for any fixed mapb: . Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categoriesH b andH b whereH b is the dual ofH b . One of our results isN b P b . This differs fromP B N B . Supported by National Natural Science Foundation of China  相似文献   

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Houjun Zhang 《代数通讯》2020,48(2):467-483
Abstract

In this article, we investigate the Gorenstein global dimension with respect to the recollements of abelian categories. With the invariants spli and silp of the categories, we give some upper bounds of Gorenstein global dimensions of the categories involved in a recollement of abelian categories. We apply our results to some rings and artin algebras, especially to the triangular matrix artin algebras.  相似文献   

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Using a backtracking algorithm along with an essential change to the rows of representatives of known 13 710 027 equivalence classes of Hadamard matrices of order 32, we make an exhaustive computer search feasible and show that there are exactly 6662 inequivalent skew‐Hadamard matrices of order 32. Two skew‐Hadamard matrices are considered SH ‐equivalent if they are similar by a signed permutation matrix. We determine that there are precisely 7227 skew‐Hadamard matrices of order 32 up to SH ‐equivalence. This partly settles a problem posed by Kim and Solé. As a consequence, we provide the classification of association schemes of order 31.  相似文献   

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We give a 3-universal property for the Karoubi envelope of a 2-category. Using this, we show that the 3-categories of finite semisimple 2-categories (as introduced in [1]) and of multifusion categories are equivalent.  相似文献   

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We show that each category enriched in Abelian groupoids is a linear track extension and hence is determined up to weak equivalence by a characteristic chomology class. We also discuss compatibility with coproducts.  相似文献   

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We study invariants of simultaneous similarity of a pair of matrices of even order 2k over the field of complex numbers for the case in which all elementary divisors of the corresponding characteristic polynomial matrix are identical and their number is k.  相似文献   

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The main goal of this paper is to prove that the idempotent completions of triangulated categories of singularities of two schemes are equivalent if the formal completions of these schemes along singularities are isomorphic. We also discuss Thomason's theorem on dense subcategories and a relation to the negative K-theory.  相似文献   

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In this paper, we investigate Hadamard matrices of order 2(p + 1) with an automorphism of odd prime order p. In particular, the classification of such Hadamard matrices for the cases p = 19 and 23 is given. Self‐dual codes related to such Hadamard matrices are also investigated. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 367–380, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10052  相似文献   

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It is known that all doubly‐even self‐dual codes of lengths 8 or 16, and the extended Golay code, can be constructed from some binary Hadamard matrix of orders 8, 16, and 24, respectively. In this note, we demonstrate that every extremal doubly‐even self‐dual [32,16,8] code can be constructed from some binary Hadamard matrix of order 32. © 2004 Wiley Periodicals, Inc.  相似文献   

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Peter R. Jones 《代数通讯》2017,45(3):1037-1056
The variety of restriction semigroups may be most simply described as that generated from inverse semigroups (S, ·, ?1) by forgetting the inverse operation and retaining the two operations x+ = xx?1 and x* = x?1x. The subvariety B of strict restriction semigroups is that generated by the Brandt semigroups. At the top of its lattice of subvarieties are the two intervals [B2, B2M = B] and [B0, B0M]. Here, B2 and B0 are, respectively, generated by the five-element Brandt semigroup and that obtained by removing one of its nonidempotents. The other two varieties are their joins with the variety of all monoids. It is shown here that the interval [B2, B] is isomorphic to the lattice of varieties of categories, as introduced by Tilson in a seminal paper on this topic. Important concepts, such as the local and global varieties associated with monoids, are readily identified under this isomorphism. Two of Tilson's major theorems have natural interpretations and application to the interval [B2, B] and, with modification, to the interval [B0, B0M] that lies below it. Further exploration may lead to applications in the reverse direction.  相似文献   

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设R=Z/pkZ(其中k>1,p是一个奇素数),A是R上一个给定的可相似对角化的n阶矩阵.利用组合方法和有限局部环上的矩阵方法,讨论了矩阵A的拓展广义逆,得到了矩阵A的拓展广义逆存在的充要条件和一些的计数定理.  相似文献   

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Fei Xu 《Advances in Mathematics》2008,219(6):1872-1893
Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C|=BC. We study the ring homomorphism HH(kC)→H(|C|,k) and prove it is split surjective, using the factorization category of Quillen [D. Quillen, Higher algebraic K-theory I, in: Lecture Notes in Math., vol. 341, Springer-Verlag, Berlin, 1973, pp. 85-147] and certain techniques from functor cohomology theory. This generalizes the well-known theorems for groups and posets. Based on this result, we construct a seven-dimensional category algebra whose Hochschild cohomology ring modulo nilpotents is not finitely generated, disproving a conjecture of Snashall and Solberg [N. Snashall, Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc. 88 (3) (2004) 705-732].  相似文献   

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一个(d,r;z]-disjunct矩阵在许多领域有着极为广泛的应用.利用n阶射影平面的性质构作了(d,r;z]-disjunct矩阵,并研究了它的检错性和纠错性.  相似文献   

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