Alexander Premet's Books

The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

By: Georgia Benkart,Thomas Bradford Gregory,Alexander Premet

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The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

By: Georgia Benkart,Thomas Bradford Gregory,Alexander Premet

Volume 197, number 920 (second of 5 numbers).

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Page Count

164

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842269

ISBN 13

9780821842263

Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

By: Sergey Zelik,Alexander Mielke

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Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

By: Sergey Zelik,Alexander Mielke

The authors study semilinear parabolic systems on the full space ${\mathbb R}^n$ that admit a family of exponentially decaying pulse-like steady states obtained via translations. The multi-pulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. They prove a global center-manifold reduction theorem for the temporal evolution of such multi-pulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, The authors verify the existence of Sinai-Bunimovich space-time chaos in 1D space-time periodically forced Swift-Hohenberg equation.

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Page Count

112

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842641

ISBN 13

9780821842645

The Alexandra of Lycophron

A Literary Study

By: Charles McNelis,Alexander Sens

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The Alexandra of Lycophron

A Literary Study

By: Charles McNelis,Alexander Sens

This monograph is a literary study of Lycophron's Alexandra, whose obscurity, a quality notorious already in antiquity, has long hampered holistic approaches. Through a series of distinct but closely integrated literary studies of major aspects of the poem, including its style, its engagement with the traditions of epic and tragedy, and it's treatment of heroism and of the gods, the book explores the way the Alexandra reconfigures Greek mythology. In particular, as it is presented in Homeric epic and Athenian tragedy, in order to cast the Romans and their restoration of Trojan glory as the ultimate telos of history. In this sense, the poem emerges as an important intermediary between Homeric epic and Latin poetry, particularly Vergil's Aeneid. By rewriting specific features of the epic and tragic traditions, the Alexandra denies to Greek heroes the glory that was the traditional compensation for their suffering, while at the same time attributing to Cassandra's Trojan family honours framed in the traditional language of Greek heroism. In this sense, the figure of Cassandra, a prophetess traditionally gifted with the power of foresight but denied credibility, self-reflexively serves as a vehicle for exploring the potentials and limitations of poetry.

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Page Count

268

Publisher

Oxford University Press

Published Date

ISBN 10

0191088579

ISBN 13

9780191088575

Sugawara Operators for Classical Lie Algebras

By: Alexander Molev:

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Sugawara Operators for Classical Lie Algebras

By: Alexander Molev:

The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical -algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical -algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.

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Page Count

321

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470436590

ISBN 13

9781470436599

Book's by Alexander Premet

The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

The Alexandra of Lycophron

The Alexandra of Lycophron

Sugawara Operators for Classical Lie Algebras

Sugawara Operators for Classical Lie Algebras

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