University of Manchester

Monday 20th October 2003

Titles and speakers are as follows.

- 11.00-11.30: TEA (Brian Hartley Room, Maths Tower, floor 6)

- 11.30-12.25 pm, room G14:

Alastair Hamilton (Bristol)

Deformations of A-infinity algebras

- 12.30 pm: LUNCH

- 2.00-2.55 pm, BHR:

Revaz Kurdiani (Aberdeen)

The Leibniz algebra structure on the second tensor power of Lie algebra

- 3.00 pm: TEA (BHR)

- 3.30-4.25 pm, BHR:

Andy Tonks (UNL)

The associahedron diagonal approximation

Title: Deformations of A-infinity algebras

Abstract: Deformations of A-infinity algebras will be considered, focusing in particular on formal one-parameter deformations. A-infinity algebras will be defined via the cobar construction and the resulting effect on the calculations discussed. Hochschild cohomology of an A-infinity algebra will be defined and its relation to deformation theory explained. A type of A-infinity algebra called a Moore algebra will be introduced. These are closely related to the one dimensional A-infinity algebras considered by Kontsevich which generate the Miller-Morita-Mumford classes in the cohomology of moduli spaces of complex algebraic curves.

Slides of talk

Revaz Kurdiani (Aberdeen)

Title: The Leibniz algebra structure on the second tensor power of Lie algebra

Abstract: The notion of Leibniz algebra was introduced not very long time ago, which is a generalization of the notion of Lie algebra. It turns out that the second tensor power of Lie algebra is a Leibniz algebra. My talk will be concentrated on this Leibniz algebra. Namely the elementary properties of this algebra will be stated. Also I will describe the non-abelian second tensor power of Lie algebra constructed by Ellis [J. Pure Appl. Algebra 46(1987), 111--115 and Glasgow Math. J. 33(1991), 101--120] (non-abelian tensor product of groups was introduced by Brown and Loday in [Topology 26(1987), 311--335]). Moreover, the maximal Lie algebra quotient of studied Leibniz algebra is an abelian extension of the non-abelian second tensor power of Lie algebra. For finite dimensional semi-simple Lie algebra the kernel of this extension will be described explicitly.

Andy Tonks (London)

Title: The associahedron diagonal approximation

Abstract: The associahedra, or "Stasheff polytopes", were introduced by Jim Stasheff in 1963 for the study of homotopy associativity of H-spaces. Combinatorially their cells correspond to bracketings or to planar rooted trees, and their vertices are counted by the Catalan numbers. The associahedron diagonal approximation, recently introduced in preprints of Saneblidze and Umble, can be seen as a generalising both the classical (simplicial) Alexander-Whitney diagonal approximation and the obvious cubical diagonal approximation. In this talk I will discuss some geometric and combinatorial aspects of these diagonal approximations, and their relation with loop spaces, cobar constructions, and the Baues conjecture on the homotopy type of certain order complexes.

Lunch will be taken locally (at the vegetarian "On the Eight Day", for example), and we expect to visit a local curry house (or similar) early in the evening.

Everyone who wishes to participate is welcome: we shall operate the usual arrangements for assistance with travel expenses. Please email Nige Ray nige@ma.man.ac.uk (or John Greenlees j.greenlees@sheffield.ac.uk, or John Hunton jrh7@mcs.le.ac.uk) if you are interested in attending, so that we can cater for appropriate numbers.

The meeting is partially supported by a Scheme 3 grant from the London Mathematical Society.

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