Structure of the rational monoid algebra for Boolean matrices of order 3

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• 作者：Murray R. Bremner¹ ; ² ; ^{bremner@math.usask.ca" class="auth_mail}
• 关键词：primary ; 15B34 ; secondary ; 16-04 ; 16G10 ; 16N99 ; 16Z05 ; 20M30 ; 68W30
• 刊名：Linear Algebra and its Applications
• 出版年：15 May, 2014
• 年：2014
• 卷：449
• 期：Complete
• 页码：381-401
• 全文大小：320 K

文摘

We use the computer algebra system Maple to study the 512-dimensional associative algebra , the rational monoid algebra of Boolean matrices. Using the LLL algorithm for lattice basis reduction, we obtain a basis for the radical in bijection with the 42 non-regular elements of . The center of the 470-dimensional semisimple quotient has dimension 14; we use a splitting algorithm to find a basis of orthogonal primitive idempotents. We show that the semisimple quotient is the direct sum of simple two-sided ideals isomorphic to matrix algebras for . We construct the irreducible representations of over by calculating the representation matrices for a minimal set of generators.