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Title: Balanced systems of primitive idempotents in matrix algebras

Abstract

The article develops the concept of balanced t-systems of idempotents in associative semisimple finite-dimensional algebras over the field of complex numbers C this was introduced by the author as a generalization of the concept of combinatorial t-schemes, which in this context corresponds to the case of commutative algebras. Balanced 2-systems are considered consisting of v primitive idempotents in the matrix algebra M{sub n}(C), known as (v,n)-systems. It is proved that (n+1,n)-systems are unique and it is shown that there are no (n+s,n)-systems with n>s{sup 2}-s or s>n{sup 2}-n. The (q+1,n)-systems having 2-transitive automorphism subgroup PSL(2,q), q odd, are classified. The (4,2)- and (6,3)-systems are classified. A balanced basis is constructed in the algebras M{sub n}, n=2,3. Connections are established between conference matrices and (2n,n)-systems.

Authors:
 [1]
  1. M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
21202927
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 191; Journal Issue: 4; Other Information: DOI: 10.1070/SM2000v191n04ABEH000471; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; MATRICES; PHOTOLUMINESCENCE

Citation Formats

Ivanov, D N. Balanced systems of primitive idempotents in matrix algebras. United States: N. p., 2000. Web. doi:10.1070/SM2000V191N04ABEH000471; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Ivanov, D N. Balanced systems of primitive idempotents in matrix algebras. United States. doi:10.1070/SM2000V191N04ABEH000471; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Ivanov, D N. Sun . "Balanced systems of primitive idempotents in matrix algebras". United States. doi:10.1070/SM2000V191N04ABEH000471; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21202927,
title = {Balanced systems of primitive idempotents in matrix algebras},
author = {Ivanov, D N},
abstractNote = {The article develops the concept of balanced t-systems of idempotents in associative semisimple finite-dimensional algebras over the field of complex numbers C this was introduced by the author as a generalization of the concept of combinatorial t-schemes, which in this context corresponds to the case of commutative algebras. Balanced 2-systems are considered consisting of v primitive idempotents in the matrix algebra M{sub n}(C), known as (v,n)-systems. It is proved that (n+1,n)-systems are unique and it is shown that there are no (n+s,n)-systems with n>s{sup 2}-s or s>n{sup 2}-n. The (q+1,n)-systems having 2-transitive automorphism subgroup PSL(2,q), q odd, are classified. The (4,2)- and (6,3)-systems are classified. A balanced basis is constructed in the algebras M{sub n}, n=2,3. Connections are established between conference matrices and (2n,n)-systems.},
doi = {10.1070/SM2000V191N04ABEH000471; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 4,
volume = 191,
place = {United States},
year = {2000},
month = {4}
}