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Lie structure of smash products
Get PDFWe investigate the conditions under which the smash product of an (ordinary or restricted) enveloping algebra and a group algebra is Lie solvable or Lie nilpotent
Lie identities on symmetric elements of restricted enveloping algebras
No full textLet L be a restricted Lie algebra over a field of characteristic p>2 and denote by u(L) its restricted enveloping algebra. We determine the conditions under which the set of symmetric elements of u(L) with respect to the principal involution is Lie solvable, Lie nilpotent, or bounded Lie Engel
Perfect and semiperfect restricted enveloping algebras
No full textFor a restricted Lie algebra L, the conditions under which its restricted enveloping algebra u(L) is semiperfect are investigated. Moreover, it is proved that u(L) is left (or right) perfect if and only if L is finite-dimensional
Restricted enveloping algebras whose skew and symmetric elements are Lie metabelian
No full textLet L be a restricted Lie algebra over a field of characteristic p > 2 and denote by u(L) its restrictedenveloping algebra. We establish when the symmetric or skew elements of u(L) under the principal involution are Lie metabelian
Lie solvable enveloping algebras of characteristic two
Get PDFLie solvable restricted enveloping algebras were characterized by Riley and Shalev except when the ground field is of characteristic 2. We resolve the characteristic 2 case here which completes the classification. As an application of our result, we obtain a characterization of ordinary Lie algebras over any field whose enveloping algebra is Lie solvable
Subideals of Lie superalgebras
No full textAbstractWe consider some questions about subnormal subgroups of a group in the setting of Lie superalgebras. In particular, the analogues of Nilpotence Join Theorem and Rosebladeʼs Theorem for Lie superalgebras are proved
Universal enveloping algebras of the four-dimensional Malcev algebra
Get PDFWe determine structure constants for the universal nonassociative enveloping algebra U(M) of the four-dimensional non-Lie Malcev algebra M by constructing a representation of U(M) by differential operators on the polynomial algebra P (M). These structure constants involve Stirling numbers of the second kind. This work is based on the recent theorem of Pérez-Izquierdo and Shestakov which generalizes the Poincaré-Birkhoff-Witt theorem from Lie algebras to Malcev algebras. We use our results for U(M) to determine structure constants for the universal alternative enveloping algebra A(M) = U(M)/I(M) where I(M) is the alternator ideal of U(M). The structure constants for A(M) were obtained earlier by Shestakov using different methods.This article is published as Bremner, Murray R., Irvin R. Hentzel, Luiz A. Peresi, and Hamid Usefi. "Universal enveloping algebras of the four-dimensional Malcev algebra." Contemporary Mathematics 483 (2009): 73-89. Posted with permission.</p
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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