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14
SIMPLE LIE SUPERALGEBRAS AND NONINTEGRABLE DISTRIBUTIONS IN CHARACTERISTIC p
, 2006
"... Abstract. Recently, Grozman and Leites returned to the original Cartan’s description of Lie algebras to interpret the Melikyan algebras (for p≤5) and several other littleknown simple Lie algebras over algebraically closed fields for p = 3 as subalgebras of Lie algebras of vector fields preserving n ..."
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Abstract. Recently, Grozman and Leites returned to the original Cartan’s description of Lie algebras to interpret the Melikyan algebras (for p≤5) and several other littleknown simple Lie algebras over algebraically closed fields for p = 3 as subalgebras of Lie algebras of vector fields preserving nonintegrable distributions analogous to (or identical with) those preserved by G(2), O(7), Sp(4) and Sp(10). The description was performed in terms of CartanTanakaShchepochkina prolongs using Shchepochkina’s algorithm and with the help of SuperLie package. Grozman and Leites also found two new series of simple Lie algebras. Here we apply the same method to distributions preserved by one of the two exceptional simple finite dimensional Lie superalgebras over C; for p = 3, we obtain a series of new simple Lie superalgebras and an exceptional one. In memory of Felix Aleksandrovich Berezin F. A. Berezin and supersymmetries are usually associated with physics. However, Lie superalgebras — infinitesimal supersymmetries — appeared in topology at approximately the same time as the word “spin ” appeared in physics and it were these examples that Berezin first had in mind.
Computing Cocycles on Simplicial Complexes
"... In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20,21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we ..."
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Cited by 3 (1 self)
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In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20,21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we give here an algorithm for computing cupi products over integers on a simplicial complex at chain level. 1
Deformed diagonal harmonic polynomials for complex reflection groups
 In 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC
, 2011
"... Abstract. We introduce deformations of the space of (multidiagonal) harmonic polynomials for any finite complex reflection group of the form W = G(m, p, n), and give supporting evidence that this space seems to always be isomorphic, as a graded Wmodule, to the undeformed version. Résumé. Nous intr ..."
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Cited by 2 (2 self)
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Abstract. We introduce deformations of the space of (multidiagonal) harmonic polynomials for any finite complex reflection group of the form W = G(m, p, n), and give supporting evidence that this space seems to always be isomorphic, as a graded Wmodule, to the undeformed version. Résumé. Nous introduisons une déformation de l’espace des polynômes harmoniques (multidiagonaux) pour tout groupe de réflexions complexes de la forme W = G(m, p, n), et soutenons l’hypothèse que cet espace est toujours isomorphe, en tant que Wmodule gradué, à l’espace d’origine.
Characterizing Frobenius Semigroups by Filtration
 JOURNAL OF INTEGER SEQUENCES, VOL. 12 (2009), ARTICLE 09.1.2
, 2009
"... For a given base a, and for all integers k, we consider the sets Ga(k) = {a k, a k + a k−1,...,a k + a k−1 + · · · + a 1 + a 0}, and for each Ga(k) the corresponding “Frobenius set” Fa(k) = {n ∈ N  n is not a sum of elements of Ga(k)}. The sets Fa(k) are nested and their union is N. Given an in ..."
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For a given base a, and for all integers k, we consider the sets Ga(k) = {a k, a k + a k−1,...,a k + a k−1 + · · · + a 1 + a 0}, and for each Ga(k) the corresponding “Frobenius set” Fa(k) = {n ∈ N  n is not a sum of elements of Ga(k)}. The sets Fa(k) are nested and their union is N. Given an integer n, we find the smallest k such that n ∈ Fa(k).
Steenrod operations on Schubert classes
, 2003
"... Let G be a compact connected Lie group and H the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan numbers of G. ..."
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Let G be a compact connected Lie group and H the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan numbers of G.
DICKSON INVARIANTS IN THE IMAGE OF THE STEENROD SQUARE
, 2000
"... Abstract. Let Dn be the Dickson invariant ring of F2[X1,..., Xn] acted by the general linear group GL(n, F2). In this paper, we provide an elementary proof of the conjecture by [3]: each element in Dn is in the image of the Steenrod square in F2[X1,..., Xn], where n> 3. 1. ..."
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Abstract. Let Dn be the Dickson invariant ring of F2[X1,..., Xn] acted by the general linear group GL(n, F2). In this paper, we provide an elementary proof of the conjecture by [3]: each element in Dn is in the image of the Steenrod square in F2[X1,..., Xn], where n> 3. 1.
Rocío González–Díaz, Pedro Real Universidad de Sevilla, Depto. de Matemática Aplicada I,
, 2001
"... In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20, 21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we ..."
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In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20, 21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we give here an algorithm for computing cup–i products over integers on a simplicial complex at chain level. 1
arXiv version: fonts
, 2007
"... pagination and layout may vary from GTM published version An algebraic introduction to the Steenrod algebra ..."
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pagination and layout may vary from GTM published version An algebraic introduction to the Steenrod algebra