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Author: William M. McGovern
Publisher: American Mathematical Soc.
ISBN: 0821825801
Category : Mathematics
Languages : en
Pages : 82
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Book Description
Let [Fraktur lowercase]g be a complex simple Lie algebra of classical type, [italic capital]U([Fraktur lowercase]g) its enveloping algebra. We classify the completely prime maximal spectrum of [italic capital]U([Fraktur lowercase]g). We also construct some interesting algebra extensions of primitive quotients of [italic capital]U([Fraktur lowercase]g), and compute their Goldie ranks, lengths as bimodules, and characteristic cycles. Finally, we study the relevance of these algebras to D. Vogan's program of "quantizing" covers of nilpotent orbits [script]O in [Fraktur lowercase]g[superscript]*.
Author: William M. McGovern
Publisher: American Mathematical Soc.
ISBN: 0821825801
Category : Mathematics
Languages : en
Pages : 82
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Book Description
Let [Fraktur lowercase]g be a complex simple Lie algebra of classical type, [italic capital]U([Fraktur lowercase]g) its enveloping algebra. We classify the completely prime maximal spectrum of [italic capital]U([Fraktur lowercase]g). We also construct some interesting algebra extensions of primitive quotients of [italic capital]U([Fraktur lowercase]g), and compute their Goldie ranks, lengths as bimodules, and characteristic cycles. Finally, we study the relevance of these algebras to D. Vogan's program of "quantizing" covers of nilpotent orbits [script]O in [Fraktur lowercase]g[superscript]*.
Author: William M. McGovern
Publisher: American Mathematical Soc.
ISBN: 9780821862421
Category : Mathematics
Languages : en
Pages : 84
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Book Description
This monograph will appeal to graduate students and researchers interested in Lie algebras. McGovern classifies the completely prime maximal spectrum of the enveloping algebra of any classical semisimple Lie algebra. He also studies finite algebra extensions of completely prime primitive quotients of such enveloping algebras and computes their lengths as bimodules, characteristic cycles, and Goldie ranks in many cases. This work marks a major advance in the quantization program, which seeks to extend the methods of (commutative) algebraic geometry to the setting of enveloping algebras. While such an extension cannot be completely carried out, this work shows that many partial results are available.
Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 0821825836
Category : Mathematics
Languages : en
Pages : 118
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Book Description
New methods are developed to describe prime ideals in skew polynomial rings [italic capital]S = [italic capital]R[[italic]y; [lowercase Greek]Tau, [lowercase Greek]Delta]], for automorphisms [lowercase Greek]Tau and [lowercase Greek]Tau-derivations [lowercase Greek]Delta] of a noetherian coefficient ring [italic capital]R.
Author: Hans Plesner Jakobsen
Publisher: American Mathematical Soc.
ISBN: 0821825933
Category : Mathematics
Languages : en
Pages : 129
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Book Description
This work contains a complete description of the set of all unitarizable highest weight modules of classical Lie superalgebras. Unitarity is defined in the superalgebraic sense, and all the algebras are over the complex numbers. Part of the classification determines which real forms, defined by anti-linear anti-involutions, may occur. Although there have been many investigations for some special superalgebras, this appears to be the first systematic study of the problem.
Author: Christian Ballot
Publisher: American Mathematical Soc.
ISBN: 0821826107
Category : Mathematics
Languages : en
Pages : 117
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Book Description
A general density theory of the set of prime divisors of a certain family of linear recurring sequences with constant coefficients, a family which is defined for any order recursion, is built up from the work of Lucas, Laxton, Hasse, and Lagarias. In particular, in this theory the notion of the rank of a prime divisor as well as the notion of a Companion Lucas sequence (Lucas), the group associated with a given second-order recursion (Laxton), and the effective computation of densities (Hasse and Lagarias) are first combined and then generalized to any order recursion.
Author: John Lindsay Orr
Publisher: American Mathematical Soc.
ISBN: 0821804057
Category : Mathematics
Languages : en
Pages : 65
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Book Description
Immersive environments such as virtual reality technology makes possible can respond to their audiences, so that each person's experience of the environment is unique. This volume brings together 11 essays along with artists' projects produced at the Banff Centre for the Arts in Canada to explore issues raised by the creation of virtual environments. The essays approach the social and cultural implications of cyberspace from the perspective of cultural studies, communications, art history, art criticism, English, and women's studies; while artists who created nine virtual worlds at the Banff Centre discuss what they have tried to accomplish in both theoretical and technical terms. With 64 illustrations, including 18 color plates. Annotation copyright by Book News, Inc., Portland, OR
Author: Anthony Joseph
Publisher: Springer Science & Business Media
ISBN: 3642784003
Category : Mathematics
Languages : en
Pages : 394
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Book Description
by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat egory of (!; modules. This means of course just defining an algebra structure on Rq[G]; but this is to be done in a very specific manner. Concretely the category is required to be braided and this forces (9.4.2) the existence of an "R-matrix" satisfying in particular the quantum Yang-Baxter equation and from which the algebra structure of Rq[G] can be written down (9.4.5). Finally there was a search for a perfectly self-dual model for Rq[G] which would then be isomorphic to Uq(g). Apparently this failed; but V. G. Drinfeld found that it could be essentially made to work for the "Borel part" of Uq(g) denoted U (b) and further found a general construction (the Drinfeld double) q mirroring a Lie bialgebra. This gives Uq(g) up to passage to a quotient. One of the most remarkable aspects of the above superficially different ap proaches is their extraordinary intercoherence. In particular they essentially all lead for G semisimple to the same and hence "canonical", objects Rq[G] and Uq(g), though this epithet may as yet be premature.
Author: Mauro Beltrametti
Publisher: American Mathematical Soc.
ISBN: 0821802348
Category : Mathematics
Languages : en
Pages : 79
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Book Description
This work studies the adjunction theory of smooth 3-folds in P]5. Because of the many special restrictions on such 3-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the 3-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such 3-folds up to degree 12 are included. Many of the general results are shown to hold for smooth projective n-folds embedded in P]N with N 2n -1.
Author: Shirō Gotō
Publisher: American Mathematical Soc.
ISBN: 0821825844
Category : Mathematics
Languages : en
Pages : 149
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Book Description
At first, this volume was intended to be an investigation of symbolic blow-up rings for prime ideals defining curve singularities. The motivation for that has come from the recent 3-dimensional counterexamples to Cowsik's question, given by the authors and Watanabe: it has to be helpful, for further researches on Cowsik's question and a related problem of Kronecker, to generalize their methods to those of a higher dimension. However, while the study was progressing, it proved apparent that the framework of Part I still works, not only for the rather special symbolic blow-up rings but also in the study of Rees algebras R(F) associated to general filtrations F = {F[subscript]n} [subscript]n [subscript][set membership symbol][subscript bold]Z of ideals. This observation is closely explained in Part II of this volume, as a general ring-theory of Rees algebras R(F). We are glad if this volume will be a new starting point for the further researchers on Rees algebras R(F) and their associated graded rings G(F).
Author: Christian Krattenthaler
Publisher: American Mathematical Soc.
ISBN: 0821826131
Category : Mathematics
Languages : en
Pages : 122
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Book Description
A theory of counting nonintersecting lattice paths by the major index and its generalizations is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given final points, where the starting points lie on a line parallel to [italic]x + [italic]y = 0. In some cases these determinants can be evaluated to result in simple products. As applications we compute the generating function for tableaux with [italic]p odd rows, with at most [italic]c columns, and with parts between 1 and [italic]n. Moreover, we compute the generating function for the same kind of tableaux which in addition have only odd parts. We thus also obtain a closed form for the generating function for symmetric plane partitions with at most [italic]n rows, with parts between 1 and [italic]c, and with [italic]p odd entries on the main diagonal. In each case the result is a simple product. By summing with respect to [italic]p we provide new proofs of the Bender-Knuth and MacMahon (ex-)conjectures, which were first proved by Andrews, Gordon, and Macdonald. The link between nonintersecting lattice paths and tableaux is given by variations of the Knuth correspondence.
