1,325 research outputs found
Mishchenko-Fomenko Subalgebras in S(gl_n) and regular sequences
No full textSeja S(gl_n) a álgebra simétrica da álgebra de Lie das matrizes de tamanho nxn sobre o corpo C dos números complexos. Para \\xi em gl_n*=gl_n, seja F_{\\xi}(gl_n) a asubálgebra de Mishchenko-Fomenko de S(gl_n) construída pelo método de deslocamento de argumento associada ao parâmetro \\xi. É conhecido que se \\xi é um elemento semisimples regular ou nilpotente regular então a subálgebra F_{\\xi}(gl_n) é gerada por uma sequência regular em S(gl_n). Nesta tese é provado que em gl_3 o resultado estende para todo \\xi em gl_3, isto é, as subálgebras de Mishchenco-Fomenko F_{\\xi}(gl_3) são geradas por uma sequência regular em S(gl_3), uma consequência deste fato é que os módulo irredutíveis sobre certas subálgebras comutativas da álgebra envolvente universal U(gl_3) podem ser levantados a módulos irredutiveis sobre U(gl_3). Além disso, é provado que em gl_4 esse resultado é válido para todo elemento nilpotente \\xi em gl_4. O caso geral, que é determinar quando as subálgebras de Mishchenko-Fomenko F_{\\xi}(gl_n) , com \\xi em gl_n, são geradas por uma sequência regular em S(gl_n), é ainda um problema aberto.Let S(gl_n) be the symmetric algebra of the Lie algebra of the matrices of size nxn over the field C of complex numbers. For \\xi in gl_n*=gl_n, let F_{\\xi}(gl_n) be the Mishchenko-Fomenko subalgebra of S(gl_n) constructed by the argument shift method associated with the parameter \\xi. It is known that if \\xi is a semisimple regular element or nilpotent regular element then the subalgebra F_(g_ln) is generated by a regular sequence in S(gl_n). In this thesis we prove that in gl_3 the result is extended to all \\xi in gl_3, this is, the Mishchenco-Fomenko subalgebras F_{\\xi}(gl3) are generated by a regular sequence in S(gl_3), A consequence of this fact is that the irreducible modules over certain commutative subalgebras of the universal enveloping algebra U(gl_3) can it be lifted to irreducible modules over U(gl_3). Furthermore, is proved that this result is true for all elements nilpotente \\xi in gl_4. The general case, which is determined when the Mishchenko-Fomenko subalgebras F_{\\xi}(gl_n), with \\xi in gl_n, are generated by a regular sequence in S(gl_n), it is still an open problem
Mishchenko-Fomenko Subalgebras in S(gl_n) and regular sequences
No full textSeja S(gl_n) a álgebra simétrica da álgebra de Lie das matrizes de tamanho nxn sobre o corpo C dos números complexos. Para \\xi em gl_n*=gl_n, seja F_{\\xi}(gl_n) a asubálgebra de Mishchenko-Fomenko de S(gl_n) construída pelo método de deslocamento de argumento associada ao parâmetro \\xi. É conhecido que se \\xi é um elemento semisimples regular ou nilpotente regular então a subálgebra F_{\\xi}(gl_n) é gerada por uma sequência regular em S(gl_n). Nesta tese é provado que em gl_3 o resultado estende para todo \\xi em gl_3, isto é, as subálgebras de Mishchenco-Fomenko F_{\\xi}(gl_3) são geradas por uma sequência regular em S(gl_3), uma consequência deste fato é que os módulo irredutíveis sobre certas subálgebras comutativas da álgebra envolvente universal U(gl_3) podem ser levantados a módulos irredutiveis sobre U(gl_3). Além disso, é provado que em gl_4 esse resultado é válido para todo elemento nilpotente \\xi em gl_4. O caso geral, que é determinar quando as subálgebras de Mishchenko-Fomenko F_{\\xi}(gl_n) , com \\xi em gl_n, são geradas por uma sequência regular em S(gl_n), é ainda um problema aberto.Let S(gl_n) be the symmetric algebra of the Lie algebra of the matrices of size nxn over the field C of complex numbers. For \\xi in gl_n*=gl_n, let F_{\\xi}(gl_n) be the Mishchenko-Fomenko subalgebra of S(gl_n) constructed by the argument shift method associated with the parameter \\xi. It is known that if \\xi is a semisimple regular element or nilpotent regular element then the subalgebra F_(g_ln) is generated by a regular sequence in S(gl_n). In this thesis we prove that in gl_3 the result is extended to all \\xi in gl_3, this is, the Mishchenco-Fomenko subalgebras F_{\\xi}(gl3) are generated by a regular sequence in S(gl_3), A consequence of this fact is that the irreducible modules over certain commutative subalgebras of the universal enveloping algebra U(gl_3) can it be lifted to irreducible modules over U(gl_3). Furthermore, is proved that this result is true for all elements nilpotente \\xi in gl_4. The general case, which is determined when the Mishchenko-Fomenko subalgebras F_{\\xi}(gl_n), with \\xi in gl_n, are generated by a regular sequence in S(gl_n), it is still an open problem
A Leibniz variety with almost polynomial growth
No full textLet F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras
V defined by the identity y1(y2y3)(y4y5) ≡ 0. We give a complete description of the space of
multilinear identities in the language of Young diagrams through the representation theory of the
symmetric group. As an outcome we show that the variety V has almost polynomial growth, i.e.,
the sequence of codimensions of V cannot be bounded by any polynomial function but any proper
subvariety of V has polynomial growt
An almost nilpotent variety of exponent 2
No full textWe construct a non-associative algebra A over a field of characteristic zero with the following properties: if V is the variety generated by A, then V has exponential growth but any proper subvariety of V is nilpotent.
Moreover, by studying the asymptotics of the sequence of codimensions of A we deduce that exp(V) = 2
Glyptobothrus maritimus Mishchenko 1951
No full textGlyptobothrus maritimus (Mishchenko, 1951) Chorthippus biguttulus maritimus Mishchenko, in Bey-Bienko & Mishchenko, 1951: 514 (Russia: Krivoi Klyuch, Korea); Tsyplenkov, 1970: 214; Rentz & Miller, 1971: 263; Storozhenko, 1986: 301; Ju et al. 1993: 287; Kwon & Huh, 1994: 52; Huh & Kwon, 1995: 13; Kwon et al. 1996: 105; Glyptobothrus maritimus: Storozhenko, 2002: 7; Storozhenko & Paik, 2007: 177; Paik et al. 2010: 54. Specimens examined (8 Ƥ ). Chann-Pay plateau Samziyon 1,600 m, 25 viii 1971, S. Horvatovich & J. Papp (No. 197); Pyongyan city park between River Te-dong and Pyongyan Hotel, 4 viii 1971, S. Horvatovich & J. Papp (No. 137); Mt. Kumgangsan path to Kuryong falls, 18 ix 1980, L. Forró & Gy. Topál (No. 692); Mt. Kumgangsan foot-path to Manmulsang Rocks, 19 ix 1980, L. Forró & Gy. Topál (No. 710).Published as part of Kim, Tae-Woo & Puskás, Gellért, 2012, Check-list of North Korean Orthoptera Based on the Specimens Deposited in the Hungarian Natural History Museum, pp. 1-27 in Zootaxa 3202 on pages 18-19, DOI: 10.5281/zenodo.28017
Codimension and colength sequences of algebras and growth phenomena.
No full textWe consider non necessarily associative algebras over a field of characteristic zero and their polynomial identities. Here we describe some of the results obtained in recent years on the sequence of codimensions and the sequence of colengths of an algebra
On almost nilpotent varieties of subexponential growth
No full textLet N2 be the variety of left-nilpotent algebras of index two, that is the variety of algebras satisfying the identity x(yz). ≡ 0. We introduce two new varieties, denoted by Vsym and Valt, contained in the variety N2 and we prove that Vsym and Valt are the only two varieties almost nilpotent of subexponential growth
Degrees of irreducible characters of the symmetric group and exponential growth
No full textWe consider sequences of degrees of ordinary irreducible Sncharacters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of n with leading coefficient less than one. We show that any such sequence has at least exponential growth and we compute an explicit bound
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