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1.
The concept of table algebra in the title is a real nonsingular generalized table algebra in the sense of [Z. Arad, E. Fisman, M. Muzychuk, Generalized table algebras, Israel J. Math. 114 (1999) 29–60]. In this paper we first give some definitions and facts about table algebras. It is well known that every association scheme gives a Hecke-algebra which is a table algebra too. This leads to the natural question which properties of association schemes stay valid for table algebras. For instance, we prove the Second Isomorphism Theorem and the Jordan–Holder's theorem for standard table algebras. 相似文献
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3.
For integral table algebras with integral table basisT, we can consider integralR-algebraRT over a subringR of the ring of the algebraic integers. It is proved that anR-algebra isomorphism between two integral table algebras must be an integral table algebra isomorphism if it is compatible
with the so-called normalizings of the integral table algebras 相似文献
4.
A table algebra was defined in [1] in order to consider in a uniform way the common properties of conjugacy classes and irreducible
characters. Non-commutative table algebras were introduced in [5]. They generalize properties of such well-known objects as
coherent and Hecke algebras. Here we extend the main definition of a non-commutative table algebra by letting the ground field
be an integral domain. We call these algebrasgeneralized table algebras (GT-algebras, in brief). It is worth mentioning that this class of algebras includes generic Hecke-Iwahori algebras
of finite Coxeter groups. We develop the general theory for this type of algebras which includes their representation theory
and theory of closed subsets. We also study the properties of primitive integral table algebras.
This research was done at the Gelbart and Minerva Foundations through the Emmy Noether Research Institute for Mathematical
Science at Bar-Ilan University. The authors wish to thank these institutions for their support.
This author was partially supported by the Israeli Ministry of Absorption. 相似文献
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6.
Bangteng Xu 《Journal of Algebra》2011,325(1):97-131
In this paper we prove some basic structure theorems for arbitrary table algebras. In particular, we prove a Krull–Schmidt theorem for arbitrary table algebras, and give applications to association schemes. 相似文献
7.
A. Rahnamai Barghi 《Journal of Applied Mathematics and Computing》2001,8(1):71-80
The purpose of this paper is to give the classification of homogeneous integral table algebras of degree 5 containing a faithful real element of width 2. In fact, these algebras are classified to exact isomorphism, that is the sets of structure constants which arise from the given basis are completely determined. This is work towards classifying homogeneous integral table algebras of degree 5. 相似文献
8.
《Discrete Mathematics》2019,342(1):29-37
Structures of table algebras whose character tables have a zero submatrix were studied in Blau and Xu (2014) and Chen and Xu (2018). In this paper we continue the research in this direction, and investigate the conditions under which the character table with a zero submatrix yields a generalized wreath product of table algebras. Applications to association schemes are also discussed. 相似文献
9.
整表代数是群代数的推广,它的理想是群代数码的推广.本文给出了整表代数的单边理想是自正交理想的必要充分条件. 相似文献
10.
We construct new integral standard generalized table algebras from parameters of projective geometries. The algebras are noncommutative, imprimitive, and six dimensional. 相似文献
11.
The paper studies standard integral table algebras containing an element of width two. It is shown that the table subalgebra
generated by such an element is exactly isomorphic to one of the table algebras described in Main Theorems 1.1. and 1.2.
The contribution of this author is a part of his Ph.D. thesis at Bar-Ilan University under the supervision of Z. Arad and
M. Muzychuk.
This author was partially supported by the Israeli Ministry of Absorption. 相似文献
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13.
Masayoshi Yoshikawa 《代数通讯》2013,41(5):2046-2060
We will investigate the structure of noncommutative imprimitive association schemes of rank 6 and the representation of their adjacency algebras. From this investigation, we will construct new integral standard generalized table algebras with three parameters. These algebras are noncommutative, imprimitive, and 6-dimensional. 相似文献
14.
Bangteng Xu 《代数通讯》2018,46(3):1018-1031
The character theory of table algebras is not as good as the character theory of finite groups. We introduce the notion of a table algebra with a central-fusion, in which the character theory has better properties. We study conditions under which a table algebra (A,B) has a central-fusion, and its central-fusion is exactly isomorphic to the wreath product of the central-fusion of a quotient table algebra of (A,B) and another table algebra. As a consequence, we obtain a complete characterization of table algebras with exactly one irreducible character whose degree and multiplicity are not equal. Applications to association schemes are also discussed. 相似文献
15.
该文研究了m≤5时特征为2的完备域上m-维3-李代数的分类,并给出了各不同构类的具体乘法表. 相似文献
16.
Angela Antonou 《代数通讯》2013,41(6):2516-2523
We classify commutative standard table algebras (STA) with at most one nontrivial multiplicity. The main result shows that there exists exactly one nontrivial multiplicity if and only if the table basis is the wreath product of a two-dimensional subalgebra and an abelian group. The theorem applies to adjacency algebras of commutative association schemes with exactly one primitive idempotent matrix of rank greater than one. A theorem of Seitz that characterizes finite groups with exactly one irreducible representation of degree greater than one is another corollary of the main theorem. 相似文献
17.
Henrique Guzzo Junior 《代数通讯》2013,41(14):5745-5757
18.
Harvey I. Blau 《Journal of Algebra》2010,323(5):1581-1592
Two theorems on the decomposition of products in nilpotent commutative table algebras are established. This generalizes several results of Adan-Bante on the decomposition of products of irreducible characters and of conjugacy classes of finite p-groups, and extends these results to fusion rule algebras and association schemes. 相似文献
19.
L. Magnin 《Algebras and Representation Theory》2010,13(6):723-753
For any complex 6-dimensional nilpotent Lie algebra
\mathfrakg,\mathfrak{g}, we compute the strain of all indecomposable 7-dimensional nilpotent Lie algebras which contain
\mathfrakg\mathfrak{g} by the adjoining a derivation method. We get a new determination of all 7-dimensional complex nilpotent Lie algebras, allowing
to check earlier results (some contain errors), along with a cross table intertwining nilpotent 6- and 7-dimensional Lie algebras. 相似文献
20.
Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FA-presentable algebra with a single unary operation is itself FA-presentable. Furthermore, it is proven that the class of unary FA-presentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable. 相似文献