By Anthony Giaquinto (auth.), Alberto S. Cattaneo, Anthony Giaquinto, Ping Xu (eds.)

This booklet is based round larger algebraic buildings stemming from the paintings of Murray Gerstenhaber and Jim Stasheff which are now ubiquitous in a variety of components of arithmetic— comparable to algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics reminiscent of quantum box conception and string concept. those better algebraic buildings offer a typical language crucial within the examine of deformation quantization, thought of algebroids and groupoids, symplectic box idea, and masses extra. the information of upper homotopies and algebraic deformation have more and more theoretical functions and feature performed a widespread function in fresh mathematical advances. for instance, algebraic models of upper homotopies have led finally to the facts of the formality conjecture and the deformation quantization of Poisson manifolds. As saw in deformations and deformation philosophy, a easy statement is that better homotopy constructions behave far better than strict buildings.

Each contribution during this quantity expands at the principles of Gerstenhaber and Stasheff. *Higher buildings in Geometry and Physics* is meant for post-graduate scholars, mathematical and theoretical physicists, and mathematicians drawn to larger constructions.

Contributors: L. Breen, A.S. Cattaneo, M. Cahen, V.A. Dolgushev, G. Felder, A. Giaquinto, S. Gutt, J. Huebschmann, T. Kadeishvili, H. Kajiura, B. Keller, Y. Kosmann-Schwarzbach, J.-L. Loday, S.A. Merkulov, D. Sternheimer, D.E. Tamarkin, C. Torossian, B.L. Tsygan, S. Waldmann, R.N. Umble.

**Read Online or Download Higher Structures in Geometry and Physics: In Honor of Murray Gerstenhaber and Jim Stasheff PDF**

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**Additional resources for Higher Structures in Geometry and Physics: In Honor of Murray Gerstenhaber and Jim Stasheff**

**Sample text**

Algebras, bialgebras, quantum groups, and algebraic deformations. Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990), pp. 51–92, Contemp. Math. vol. 134. Am. Math. : Construction of quantum groups from Belavin-Drinfel’d inﬁnitesimals. Quantum deformations of algebras and their representations. Israel Math. Conf. Proc. vol. 7, pp. 45–64. : Bialgebra actions, twists, and universal deformation formulas. J. Pure Appl. : Deformations of sheaves of algebras.

The conference proceedings which contain the article [St97b]. : Frobenius manifolds and formality of Lie algebras of polyvector ﬁelds. Int. Math. Res. Not. 4, 201–215 (1998). : The twisted Eilenberg–Zilber theorem. Celebrazioni Archimedee del Secolo XX, In: Simposio di topologia, pp. : On the theory of elimination. Camb. Dublin Math. J. : Principal quasi-ﬁbrations and ﬁber homotopy equivalence of bundles. Illinois J. Math. : On the groups H(π, n). I. Ann. Math. 58, 55–106 (1953). II. Methods of computation.

Funktsional. Anal. i Prilozhen. : Orthogonal idempotents in the descent algebra of type Bn and applications. J. Pure Appl. : The decomposition of Hochschild cohomology and Gerstenhaber operations. J. Pure Appl. : Rankin-Cohen brackets and formal quantization. Adv. Math. : Quantum groups and deformation quantization: explicit approaches and implicit aspects. J. Math. Phys. : Poincare-Birkhoﬀ-Witt theorem for quadratic algebras of Koszul type. J. : Algebraic deformations arising from orbifolds with discrete torsion.