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Bruhat-Chevalley order on \(\mathcal{J}\) -classes of reductive monoids

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Abstract

In this paper we give an alternate description of the Bruhat-Chevalley order on \(\mathcal{J}\) -classes of the Renner monoid using Bruhat intersections. This description eliminates the Zariski closure that appears in the usual definition.

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References

  1. Deodhar, V.V.: On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat Cells. Invent. Math. 79, 499–511 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  2. Green, J.A.: On the structure of semigroups. Ann. Math. 54, 163–172 (1951)

    Article  Google Scholar 

  3. Pennell, E.A., Putcha, M.S., Renner, L.E.: Analogue of the Bruhat-Chevalley order for reductive groups. J. Algebra 196, 339–368 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Putcha, M.S.: Linear Algebraic Monoids. Cambridge University Press, Cambridge (1988)

    MATH  Google Scholar 

  5. Putcha, M.S.: A semigroup approach to linear algebraic groups. J. Algebra 80(1), 164–185 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  6. Putcha, M.S.: Shellability in reductive monoids. Trans. Am. Math. Soc. 354(1), 413–426 (2001)

    Article  MathSciNet  Google Scholar 

  7. Renner, L.E.: Linear Algebraic Monoids. Encylopaedia of Mathematical Sciences, vol. 134. Springer, Berlin (2005)

    MATH  Google Scholar 

  8. Renner, L.E.: Analogue of the Bruhat decomposition for algebraic monoids. J. Algebra 101, 303–338 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  9. Renner, L.E.: Classification of semisimple algebraic monoids. Trans. Am. Math. Soc. 292(1), 193–223 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  10. Taylor, D.T.: Fine Bruhat intersections for reductive monoids. Int. J. Algebra Comput. 16(6), 1181–1196 (2006)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, 1001 West Main St., Richmond, VA, 23284, USA

    Dewey T. Taylor

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  1. Dewey T. Taylor
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Correspondence to Dewey T. Taylor.

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Communicated by Mohan S. Putcha.

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Taylor, D.T. Bruhat-Chevalley order on \(\mathcal{J}\) -classes of reductive monoids. Semigroup Forum 78, 7–13 (2009). https://doi.org/10.1007/s00233-008-9062-8

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  • DOI: https://doi.org/10.1007/s00233-008-9062-8

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