Abdenacer Makhlouf – författare

The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers.

Each chapter combines some of the features of both a graduate level textbook and of research level surveys.

The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers.

Each chapter combines some of the features of both a graduate level textbook and of research level surveys.

Cet ouvrage regroupe les cours de la deuxième école de physique théorique de Jijel. Il porte essentiellement sur les méthodes de la théorie quantique des champs. Il est destiné aux chercheurs et enseignants ainsi qu''aux étudiants de Master physique ou mathématique désireux de connaître et d''acquérir les techniques les plus modernes. L''ouvrage contient des introductions à la théorie statistique des champs, la chromodynamique quantique perturbative et les algèbres de Hopf. Il présente le groupe de renormalisation sous ses multiples-facettes. On y aborde l''équivalence des formalismes opératoriel et fonctionnel dans sa version causale. En physique statistique, on insiste sur les aspects globaux et non perturbatifs du groupe de renormalisation en considérant la formulation de Wilson. En chromodynamique quantique perturbative, on met en valeur l''approche quantitative vis à vis de l''expérience. Enfin on présente l''approche algébrique de la renormalisation introduite par A. Connes et D. Kreimer. L''ouvrage est complété par un exposé sur l''instabilité du vide en présence des champs super-critiques, d''une discussion sur la mesure en physique quantique ainsi que d''une revue de la relativité de Poincaré replacée dans son contexte historique.

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more.

The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond.

The book benefits a broad audience of researchers and advanced students.