Results 11 to 20 of about 405 (171)
The Bruhat order on abelian ideals of Borel subalgebras [PDF]
Transactions of the American Mathematical Society, 2020 Let G G be a quasi-simple algebraic group over an algebraically closed field
Gandini, Jacopo +3 more
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B-Stable Ideals in the Nilradical of a Borel Subalgebra [PDF]
Canadian Mathematical Bulletin, 2005 AbstractWe count the number of strictly positive B-stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any B-stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We also count the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.
Eric N. Sommers
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SciPost Physics CoreWe consider the cyclic representations $\Omega_{rs}$ of $U_q(\widehat{\mathfrak{sl}}_2)$ at $q^N=1$ that depend upon two points $r,s$ in the chiral Potts algebraic curve. We show how $\Omega_{rs}$ is related to the tensor product $\rho_r\otimes \bar{\rho}
Robert Weston
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Abelian ideals of Borel subalgebras and affine Weyl groups
Advances in Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
PAPI, Paolo, Paola Cellini
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Equivalence Classes of Ideals in the Nilradical of a Borel Subalgebra [PDF]
Nagoya Mathematical Journal, 2006 AbstractAn equivalence relation is defined and studied on the set of B-stable ideals in the nilradical of the Lie algebra of a Borel subgroup B. Techniques are developed to compute the equivalence relation and these are carried out in the exceptional groups.
Sommers, E
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Very nilpotent basis and n-tuples in Borel subalgebras [PDF]
Comptes Rendus. Mathématique, 2010 A (vector space) basis B of a Lie algebra is said to be very nilpotent if all the iterated brackets of elements of B are nilpotent. In this Note, we prove a refinement of Engel's Theorem. We show that a Lie algebra has a very nilpotent basis if and only
Michaël Bulois +2 more
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Uniqueness up to inner automorphism of regular exact Borel subalgebras
Advances in MathematicsKülshammer, König and Ovsienko proved that for any quasi-hereditary algebra $(A,\leq_A)$ there exists a Morita equivalent quasi-hereditary algebra $(R, \leq_R)$ containing a basic exact Borel subalgebra $B$. The obtained Borel subalgebra is in fact a regular exact Borel subalgebra.
Rasmussen, Anna Rodriguez
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Cohomology of nilradicals of Borel subalgebras [PDF]
Transactions of the American Mathematical Society, 1974 Let 9? be the maximal nilpotent ideal in a Borel subalgebra of a complex simple Lie algebra. The cohomology groups HA91, 9M), H11(91. *) and the 9N-invariant symmetric bilinear forms on 91 are determined. The main result is the computation of H2(1,9).
Leger, George F., Luks, Eugene M.
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Elementary Lie Algebras and Lie A-Algebras. [PDF]
, 2007 A finite-dimensional Lie algebra L over a field F is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. The present paper is primarily concerned with the classification of
Varea, Vicente R., Towers, David A.
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Nuclear Physics B, 2014 We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra Uq(glˆ(M|N)). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of Uq(gl(M|N)) in the FRT formulation
Zengo Tsuboi
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