Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A CONSTRUCTION OF MAXIMAL COMMUTATIVE SUBALGEBRA OF MATRIX ALGEBRAS

  • Song, Young-Kwon (Department of Mathematics Research Institute of Basic Science)
  • Published : 2003.03.01
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Abstract

Let (B, m$_{B}$, k) be a maximal commutative $textsc{k}$-subalgebra of M$_{m}$(k). Then, for some element z $\in$ Soc(B), a k-algebra R = B［X,Y］/I, where I ＝ (m$_{B}$X, m$_{B}$Y, X$^2$- z,Y$^2$- z, XY) will create an interesting maximal commutative $textsc{k}$-subalgebra of a matrix algebra which is neither a $C_1$-construction nor a $C_2$-construction. This construction will also be useful to embed a maximal commutative $textsc{k}$-subalgebra of matrix algebra to a maximal commutative $textsc{k}$-subalgebra of a larger size matrix algebra.gebra.a.

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References

  1. Comm. Algebra v.59 no.12 Maximal Commutative Subalgebras of n×n Matrices W. C. Brown;F. W. Call
  2. Comm. Algebra v.22 no.10 Two Constructions of Maximal Commutative Subalgebras of n × n Matrices W. C. Brown https://doi.org/10.1080/00927879408825065
  3. Comm. Algebra v.25 no.12 Constructing Maximal Commutative Subalgebras of Matrix Rings in Small Dimensions W. C. Brown https://doi.org/10.1080/00927879708826096
  4. Duke Math. J. v.32 The Dimension of Maximal Commutative Subalgebras of $K_n$ R. C. Courter https://doi.org/10.1215/S0012-7094-65-03219-9
  5. Ann. of Math. v.73 no.2 On Dominance and Varieties of Commuting Matrices M. Gerstenhaber https://doi.org/10.2307/1970336
  6. Bull. of the Amer. Math. Soc. v.50 Schur’s Theorem on Commutative Matrices N. Jacobson https://doi.org/10.1090/S0002-9904-1944-08169-X
  7. Comm. Algebra v.25 no.12 On the Maximal Commutative Subalgebras of 14 by 14 Matrices Y. Song https://doi.org/10.1080/00927879708826089
  8. Comm. Algebra v.27 no.4 Maximal Commutative Subalgebras of Matrix Algebras Y. Song https://doi.org/10.1080/00927879908826519
  9. Comm. Algebra v.29 no.10 Notes on the Constructions of Maximal Commutative Subalgebra of $M_n(κ)$ Y. Song https://doi.org/10.1081/AGB-100106759

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  3. Commutative Nilpotent Subalgebras with Nilpotency Index n-1 in the Algebra of Matrices of Order n vol.224, pp.6, 2017, https://doi.org/10.1007/s10958-017-3465-6
  4. Maximal commutative subalgebras of a Grassmann algebra pp.1793-6829, 2018, https://doi.org/10.1142/S0219498819501391