A CONSTRUCTION OF MAXIMAL COMMUTATIVE SUBALGEBRA OF MATRIX ALGEBRAS

Title & Authors
A CONSTRUCTION OF MAXIMAL COMMUTATIVE SUBALGEBRA OF MATRIX ALGEBRAS
Song, Young-Kwon;

Abstract
Let (B, m$\small{_{B}}$, k) be a maximal commutative $\small{textsc{k}}$-subalgebra of M$\small{_{m}}$(k). Then, for some element z $\small{\in}$ Soc(B), a k-algebra R = B［X,Y］/I, where I ＝ (m$\small{_{B}}$X, m$\small{_{B}}$Y, X$\small{^2}$- z,Y$\small{^2}$- z, XY) will create an interesting maximal commutative $\small{textsc{k}}$-subalgebra of a matrix algebra which is neither a $\small{C_1}$-construction nor a $\small{C_2}$-construction. This construction will also be useful to embed a maximal commutative $\small{textsc{k}}$-subalgebra of matrix algebra to a maximal commutative $\small{textsc{k}}$-subalgebra of a larger size matrix algebra.gebra.a.
Keywords
C(equation omitted)-construction;
Language
English
Cited by
1.
The length function and matrix algebras, Journal of Mathematical Sciences, 2013, 193, 5, 687
2.
Classification of matrix subalgebras of length 1, Journal of Mathematical Sciences, 2012, 185, 3, 458
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