Maximality preserving constructions of maximal commutative subalgebras of matrix algebra

Youngkwon Song

doi:10.4134/BKMS.2012.49.2.295

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2012; 49(2): 295-306

Printed March 1, 2012

https://doi.org/10.4134/BKMS.2012.49.2.295

Maximality preserving constructions of maximal commutative subalgebras of matrix algebra

Youngkwon Song

Kwangwoon University

Abstract

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Abstract

Let $(R,m_{R},k)$ be a local maximal commutative subalgebra of $M_{n}(k)$ with nilpotent maximal ideal $m_{R}$. In this paper, we will construct a maximal commutative subalgebra $R^{ST}$ which is isomorphic to $R$ and study some interesting properties related to $R^{ST}$. Moreover, we will introduce a method to construct an algebra in $MC_{n}(k)$ with $i(m_{R})=n$ and $\dim (R)=n$.

Keywords: maximal commutative subalgebra, ST-isomorphism

MSC numbers: 15A27, 15A33