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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The Bruhat order on abelian ideals of Borel subalgebras
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by Jacopo Gandini, Andrea Maffei, Pierluigi Möseneder Frajria and Paolo Papi PDF
Trans. Amer. Math. Soc. 373 (2020), 6999-7018 Request permission

Abstract:

Let $G$ be a quasi-simple algebraic group over an algebraically closed field $\mathsf {k}$ whose characteristic is not very bad for $G$, and let $B$ be a Borel subgroup of $G$ with Lie algebra $\mathfrak {b}$. Given a $B$-stable abelian subalgebra $\mathfrak {a}$ of the nilradical of $\mathfrak {b}$, we parametrize the $B$-orbits in $\mathfrak {a}$ and we describe their closure relations.
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Additional Information
  • Jacopo Gandini
  • Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
  • MR Author ID: 932646
  • Email: jacopo.gandini@unibo.it
  • Andrea Maffei
  • Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
  • MR Author ID: 612173
  • Email: andrea.maffei@unipi.it
  • Pierluigi Möseneder Frajria
  • Affiliation: Politecnico di Milano, Polo regionale di Como, Via Valleggio 11, 22100 Como, Italy
  • Email: pierluigi.moseneder@polimi.it
  • Paolo Papi
  • Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
  • MR Author ID: 322097
  • Email: papi@mat.uniroma1.it
  • Received by editor(s): March 4, 2019
  • Received by editor(s) in revised form: November 21, 2019
  • Published electronically: July 28, 2020
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 6999-7018
  • MSC (2010): Primary 14M17; Secondary 14M27, 17B08
  • DOI: https://doi.org/10.1090/tran/8092
  • MathSciNet review: 4155198