Auswahl der wissenschaftlichen Literatur zum Thema „Dimension de Gelfand-Kirillov“
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Zeitschriftenartikel zum Thema "Dimension de Gelfand-Kirillov"
Zhang, Yang, und Xiangui Zhao. „Gelfand–Kirillov dimension of differential difference algebras“. LMS Journal of Computation and Mathematics 17, Nr. 1 (2014): 485–95. http://dx.doi.org/10.1112/s1461157014000102.
Der volle Inhalt der QuelleBERGEN, JEFFREY, und PIOTR GRZESZCZUK. „GK DIMENSION AND LOCALLY NILPOTENT SKEW DERIVATIONS“. Glasgow Mathematical Journal 57, Nr. 3 (18.12.2014): 555–67. http://dx.doi.org/10.1017/s0017089514000482.
Der volle Inhalt der QuelleLezama, Oswaldo, und Helbert Venegas. „Gelfand–Kirillov dimension for rings“. São Paulo Journal of Mathematical Sciences 14, Nr. 1 (24.04.2020): 207–22. http://dx.doi.org/10.1007/s40863-020-00166-4.
Der volle Inhalt der QuelleCENTRONE, LUCIO. „A NOTE ON GRADED GELFAND–KIRILLOV DIMENSION OF GRADED ALGEBRAS“. Journal of Algebra and Its Applications 10, Nr. 05 (Oktober 2011): 865–89. http://dx.doi.org/10.1142/s0219498811004987.
Der volle Inhalt der QuelleBell, Jason P., T. H. Lenagan und Kulumani M. Rangaswamy. „Leavitt path algebras satisfying a polynomial identity“. Journal of Algebra and Its Applications 15, Nr. 05 (30.03.2016): 1650084. http://dx.doi.org/10.1142/s0219498816500845.
Der volle Inhalt der QuelleZhao, Xiangui, und Yang Zhang. „Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras“. Algebra Colloquium 23, Nr. 04 (26.09.2016): 701–20. http://dx.doi.org/10.1142/s1005386716000596.
Der volle Inhalt der QuelleMoreno-Fernández, José M., und Mercedes Siles Molina. „Graph algebras and the Gelfand–Kirillov dimension“. Journal of Algebra and Its Applications 17, Nr. 05 (26.04.2018): 1850095. http://dx.doi.org/10.1142/s0219498818500950.
Der volle Inhalt der QuelleMartinez, C. „Gelfand-Kirillov dimension in Jordan Algebras“. Transactions of the American Mathematical Society 348, Nr. 1 (1996): 119–26. http://dx.doi.org/10.1090/s0002-9947-96-01528-0.
Der volle Inhalt der QuelleSmith, S. Paul, und James J. Zhang. „A remark on Gelfand-Kirillov dimension“. Proceedings of the American Mathematical Society 126, Nr. 2 (1998): 349–52. http://dx.doi.org/10.1090/s0002-9939-98-04074-x.
Der volle Inhalt der QuelleLeroy, A., und I. Matczuk. „Gelfand-Kirillov dimension of certain localizations“. Archiv der Mathematik 53, Nr. 5 (November 1989): 439–47. http://dx.doi.org/10.1007/bf01324719.
Der volle Inhalt der QuelleDissertationen zum Thema "Dimension de Gelfand-Kirillov"
Gilmartin, Paul. „Connected Hopf algebras of finite Gelfand-Kirillov dimension“. Thesis, University of Glasgow, 2016. http://theses.gla.ac.uk/7780/.
Der volle Inhalt der QuelleGalvão, Lucas. „A dimensão de Gelfand-Kirillov de certas álgebras“. Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18032015-164005/.
Der volle Inhalt der QuelleThe Gelfand-Kirillov dimension measures the asymptotic rate of growth of algebras. Since it provides important structural information, this invariant has become one of the standard tools in the study of innite dimensional algebras. In this work we present the basic properties of the Gelfand-Kirillov dimension of algebras and modules, and we also show the calculation of the Gelfand-Kirillov dimension of some algebras and modules, being the most important example the calculation of the Gelfand-Kirillov dimension of the Weyl algebra An.
Machado, Gustavo Grings 1987. „Dimensão de Gelfand-Kirillov em álgebras relativamente livres“. [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306359.
Der volle Inhalt der QuelleTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Neste trabalho estudamos o invariante denominado dimensão de Gelfand-Kirillov para álgebras com identidades polinomiais, sobretudo para álgebras não-associativas, com o objetivo de melhor compreender a estrutura das identidades polinomiais. Ultimamente este invariante tem ganhado importância, uma vez que ele é relativamente fácil de calcular e, de certa forma, é capaz de diferenciar o crescimento de duas álgebras. Para álgebras associativas a GK-dimensão mostrou-se muito útil ao detectar que álgebras que por um lado são PI-equivalentes sobre corpos de característica zero pelo Teorema do Produto Tensorial de Kemer, por outro lado não são PI-equivalentes quando a característica do corpo infinito é positiva. Isto aponta para o surgimento de novos ????-ideais, conjuntos de identidades satisfeitas por uma álgebra, que são ???? -primos para corpos infinitos de característica positiva. Ainda é um problema em aberto a classificação e a compreensão destes ????-ideais em característica positiva, embora seja bem compreendida para PI-Álgebras associativas em característica zero, segundo a teoria de Kemer. Entretanto a situação é ainda menos clara para variedades de álgebras não-associativas como Álgebras de Jordan ou Álgebras de Lie. Sabe-se muito pouco sobre resultados que apontem para uma classificação de ????-ideais fora do caso associativo, até mesmo sobre corpos de característica zero. Inclusive se conhece pouco sobre o comportamento dos ????-ideais, mesmo de álgebras simples. Aqui damos um passo, calculando algumas GK-dimensões para álgebras relativamente livres de posto finito a partir da expressão da série de Hilbert. Destacamos em especial que calculamos a dimensão de Gelfand-Kirillov da álgebra relativamente livre de qualquer posto finito da álgebra de Lie das matrizes 2 × 2 de traço zero sobre um corpo infinito de característica diferente de 2. Acreditamos que estes resultados permitirão ajudar a compreender melhor o comportamento dos ????-ideais em álgebras não-associativas
Abstract: In this thesis we study the invariant called Gelfand-Kirillov Dimension for algebras with polynomial identities, mainly for non-associative algebras, aiming at better understanding the structure of the polynomial identities. This invariant has gained importance lately since in many cases it is relatively easy to calculate and, surprisingly, it is capable of distinguishing the growth of two algebras. For associative algebras GK-dimension was found to be very useful to detect that algebras which on one hand are PI-equivalent over fields of characteristic zero, according to Tensor Product Theorem of Kemer, on the other hand are not PI-equivalent when the characteristic of the infinite base field is positive. This points towards the rise of new ????-ideals, sets of identities satisfied by an algebra, which are ????-prime for infinite fields of positive characteristic. The classification and the understanding of such ????-ideals in positive characteristic are still open problems, although it is well understood for associative PI-Algebras in characteristic zero, using Kemer¿s theory. The situation is much less clear for varieties of non-associative algebras like Jordan Algebras or Lie Algebras. Very little is known about results towards a classification of ????-ideals outside the associative case, even over fields of characteristic zero. Accordingly little is known concerning the behavior of ????-ideals, even for simple algebras. Here we make a step towards this goal by computing some GK-dimensions of some relatively free algebras of finite rank by using the expression of the Hilbert series. In particular we compute the Gelfand-Kirillov dimension of the relatively free algebra of any finite rank generated by the Lie Algebra of the 2 × 2 traceless matrices over an infinite field of characteristic different from 2. We hope that results in this direction will contribute to a better understanding of the behavior of ????-ideals in non-associative algebras
Doutorado
Matematica
Doutor em Matemática
Campbell, Chris John Montgomery. „Deformation theory of a birationally commutative surface of Gelfand-Kirillov dimension 4“. Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/22886.
Der volle Inhalt der QuelleLOBÃO, Carlos David de Carvalho. „A dimensão de Gelfand-Kirillov e algumas aplicações a PI-Teoria“. Universidade Federal de Campina Grande, 2009. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1211.
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As álgebras verbalmente primas são bem conhecidas em característica 0. Já sobre corpos de característica p > 2 pouco sabemos sobre elas. Apresentamos modelos genéricos e calcularemos a dimensão de Gelfand-kirillov para as álgebras E⊗E, Aa,b, Ma,b(E)⊗E e Ma,b(E)⊗E. Como consequência, obteremos a prova de não PI-equivalência entre álgebras importantes para PI-Teoria em características positiva.
The verbally prime algebras are well understood in characteristic 0 while over a field of characteristic p > 2 little is known about them. In this work we discuss some sharp differents between these two generics cases for the characteristc. We exhibit constructions of generic models. By using these models we compute the Gelfand-Kirillov dimension of the relatively free algebras of rank m in the varieties generated by E⊗E, Aa,b, Ma,b(E)⊗E e Ma,b(E)⊗E. As consequence we obtain the PI non equivalence of important algebras for the PI theory in positive characteristic.
Heymann-Heidelberger, Eric [Verfasser], und István [Akademischer Betreuer] Heckenberger. „The Gelfand-Kirillov dimension of rank 2 Nichols algebras of diagonal type / Eric Heymann-Heidelberger ; Betreuer: István Heckenberger“. Marburg : Philipps-Universität Marburg, 2020. http://d-nb.info/1215293240/34.
Der volle Inhalt der QuelleZhao, Xiangui. „Groebner-Shirshov bases in some noncommutative algebras“. London Mathematical Society, 2014. http://hdl.handle.net/1993/24315.
Der volle Inhalt der QuelleBois, Jean-Marie. „Corps enveloppants des algèbres de Lie en dimension infinie et en caractéristique positive“. Phd thesis, Université de Reims - Champagne Ardenne, 2004. http://tel.archives-ouvertes.fr/tel-00371835.
Der volle Inhalt der QuelleOn suppose k de caractéristique nulle. On définit d'abord la notion de "degré de transcendance de niveau q" pour les algèbres de Poisson. Cette notion est introduite à partir de la notion de dimension de niveau q définie par V. Pétrogradsky pour les algèbres associatives et les algèbres de Lie. On démontre, sous des hypothèses peu restrictives sur g, que le degré de transcendance de niveau q+1 de K(g) est égal à la dimension de niveau q de g.
On s'attache ensuite à l'étude de la famille des algèbres de type Witt définies par R. Yu. On construit ainsi des familles infinies de corps gauches deux à deux non isomorphes mais de même degré de transcendance de niveau 3 donné. On étudie aussi la question des centralisateurs dans les corps enveloppants des parties positives des algèbres de type Witt. On établit en particulier le résultat suivant : il existe des algèbres de Lie non commutatives de dimension infinie g telles que le premier corps de Weyl ne se plonge pas dans K(g).
Supposons maintenant k de caractéristique p>0. On étudie le cas particuliers des algèbres de Lie suivantes : les algèbres gl(n) ; les algèbres sl(n) lorsque p ne divise pas n ; l'algèbre de Witt modulaire W(1) et une sous-algèbre P de l'algèbre de Witt W(2) (s'identifiant à un produit tensoriel de l'algèbre de Lie W(1) avec une algèbre associative de polynômes tronqués). Dans tous les cas, on démontre que le corps enveloppant est isomorphe à un corps de Weyl. Pour les algèbres W(1) et P, on démontre en outre que le centre de l'algèbre enveloppante est un anneau factoriel, en accord avec une conjecture récente de A. Braun et C. Hajarnavis.
Sanmarco, Guillermo Luis. „Aportes a la clasificación de álgebras de Hopf punteadas de dimensión de Gelfand-Kirillov finita“. Doctoral thesis, 2020. http://hdl.handle.net/11086/17223.
Der volle Inhalt der QuelleEsta tesis es un aporte a la clasificación de las álgebras de Hopf punteadas de dimensión de Gelfand-Kirillov finita sobre cuerpos algebraicamente cerrados y de característica cero. En una primera instancia nos concentramos en álgebras de Hopf punteadas de dimensión finita sobre grupos no abelianos y cuya trenza infinitesimal no es simple. En este contexto, estudiamos un espacio vectorial trenzado particular que puede realizarse como módulo de Yetter-Drinfeld sobre una familia de grupos no abelianos y que da lugar a un álgebra de Nichols de dimensión finita. Con el objetivo de clasificar las álgebras de Hopf punteadas que tiene esta trenza infinitesimal, seguimos los pasos propuestos por el método del levante. Encontramos una presentación minimal del álgebra de Nichols, crucial para demostrar la validez de la conjetura de generación en grado 1 en nuestro contexto. Introducimos un álgebra de pre-Nichols distinguida que tiene dimensión de Gelfand-Kirillov 2 y es una extensión del álgebra de Nichols por una subálgebra de Hopf trenzada normal. Finalmente describimos todas las álgebras de Hopf punteadas de dimensión finita cuya trenza infinitesimal es la trenza en cuestión; mas aún probamos que todas ellas son deformaciones por cociclo de la correspondiente bosonización del álgebra de Nichols. En la segunda parte de esta tesis consideramos dos familias de espacios vectoriales trenzados de tipo diagonal: los de tipo Cartan y los que tienen diagrama de Dynkin completamente disconexo. El objetivo es determinar, para cada una de estas trenzas, todas las álgebras de pre-Nichols de dimensión de Gelfand-Kirillov finita. Para ello introducimos la noción de álgebras de pre-Nichols eminentes. Mostramos que, salvo algunas excepciones, las álgebras de pre-Nichols distinguidas son eminentes. Este tratamiento se asienta en el conocimiento de las relaciones que definen, en cada caso, al álgebra de pre-Nichols distinguida, y las excepciones están relacionadas con fenómenos propios de los casos en los que intervienen raíces de la unidad de orden pequeño. Para dos de los casos excepcionales mencionados anteriormente, construimos álgebras de pre-Nichols eminentes que cubren propiamente a las correspondientes distinguidas.
In a first instance we focus on finite dimensional pointed Hopf algebras over non-abelian groups and with non-simple infinitesimal braiding.In this context we study a fixed braided vector space that can be realized as Yetter-Drinfeld module over a family of non-abelian groups, and it gives rise to a finite dimensional Nichols algebra. With the purpose of classifying finite dimensional pointed Hopf algebras with this fixed infinitesimal braiding, we follow the steps proposed by the Lifting method.We find a minimal presentation by generators and relations of the Nichols algebras, which will be crucial in our proof of the validity of the generation in degree one in this context. We introduce a distinguished pre-Nichols algebra, which has Gelfand-Kirillov dimension 2 and can be obtained as an extension of the Nichols algebra by a braided normal Hopf subalgebra. Finally, we describe all finite dimensional pointed Hopf algebras with this infinitesimal braiding, furthermore we show that all of them are cocycle deformations of the corresponding bosonization of the Nichols algebra. In the second part of this thesis we consider two families of braided vector spaces of diagonal type, namely: those of Cartan type and those with totally disconnected Dynkin diagram. The goal is to determine, for each of these braidings, all their pre-Nichols algebras with finite Gelfand-Kirillov dimension. With this purpose we introduce the notion of eminent pre-Nichols algebra. We show that, up to some exceptions, the distinguished pre-Nichols algebras are in fact eminent. This treatment is based on the knowledge of the defining relations of the distinguished pre-Nichols algebra, and the exceptions are related to particular phenomena that arise when roots of unity of small orders are involved. Eminent pre-Nichols algebras are constructed for two of the aforementioned exceptional cases.
Fil: Sanmarco, Guillermo Luis. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
Fil: Sanmarco, Guillermo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas - Universidad Nacional de Córdoba. Centro de Investigaciones y Estudios de Matemática; Argentina
Bücher zum Thema "Dimension de Gelfand-Kirillov"
Krause, G. R. Growth of algebras and Gelfand-Kirillov dimension. Boston: Pitman Advanced Pub. Program, 1985.
Den vollen Inhalt der Quelle findenKrause, G. R. Growth of algebras and Gelfand-Kirillov dimension. Providence, R.I: American Mathematical Society, 2000.
Den vollen Inhalt der Quelle findenKrause, G. R. Growth of Algebras and Gelfand Kirillov-Dimension. Wiley & Sons, Incorporated, John, 1986.
Den vollen Inhalt der Quelle findenProcesi, Claudio, Eli Aljadeff, Antonio Giambruno und Amitai Regev. Rings with Polynomial Identities and Finite Dimensional Representations of Algebras. American Mathematical Society, 2020.
Den vollen Inhalt der Quelle findenBuchteile zum Thema "Dimension de Gelfand-Kirillov"
McConnell, J., und J. Robson. „Gelfand-Kirillov dimension“. In Graduate Studies in Mathematics, 297–338. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/gsm/030/09.
Der volle Inhalt der QuelleNǎstǎsescu, Constantin, und Freddy van Oystaeyen. „The Gelfand-Kirillov Dimension“. In Dimensions of Ring Theory, 313–42. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3835-9_11.
Der volle Inhalt der QuelleKrause, Günter, und Thomas Lenagan. „Gelfand-Kirillov dimension of algebras“. In Graduate Studies in Mathematics, 13–22. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/gsm/022/03.
Der volle Inhalt der QuelleKrause, Günter, und Thomas Lenagan. „Gelfand-Kirillov dimension of related algebras“. In Graduate Studies in Mathematics, 23–35. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/gsm/022/04.
Der volle Inhalt der QuelleGranja, Ángel, José Ángel Hermida und Alain Verschoren. „Computing the Gelfand-Kirillov Dimension II“. In Ring Theory And Algebraic Geometry, 33. Boca Raton: CRC Press, 2001. http://dx.doi.org/10.1201/9780203907962-2.
Der volle Inhalt der QuelleBueso, José, José Gómez-Torrecillas und Alain Verschoren. „The Gelfand-Kirillov dimension and the Hilbert polynomial“. In Algorithmic Methods in Non-Commutative Algebra, 239–61. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0285-0_7.
Der volle Inhalt der QuelleMcConnell, J. C. „Quantum groups, filtered rings and Gelfand-Kirillov dimension“. In Lecture Notes in Mathematics, 139–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0091258.
Der volle Inhalt der QuelleMatczuk, J. „The Gelfand-Kirillov Dimension of Poincare-Birkhoff-Witt Extensions“. In Perspectives in Ring Theory, 221–26. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2985-2_18.
Der volle Inhalt der QuelleWallach, Nolan R. „On the Gelfand–Kirillov dimension of a discrete series representation“. In Representations of Reductive Groups, 505–16. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23443-4_18.
Der volle Inhalt der QuelleMcConnell, J. C., und J. C. Robson. „Gelfand-Kirillov Dimension, Hilbert-Samuel polynomials and Rings of Differential Operators“. In Perspectives in Ring Theory, 233–38. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2985-2_20.
Der volle Inhalt der QuelleKonferenzberichte zum Thema "Dimension de Gelfand-Kirillov"
Mao, Lingling. „The Gelfand-kirillov Dimension of Quantized enveloping Algebra of Uq(B2)“. In 2019 IEEE International Conference on Computation, Communication and Engineering (ICCCE). IEEE, 2019. http://dx.doi.org/10.1109/iccce48422.2019.9010783.
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