11,445 research outputs found
The modular isomorphism problem for finite -groups with a cyclic subgroup of index
Let be a prime number, be a finite -group and be a field of
characteristic . The Modular Isomorphism Problem (MIP) asks whether the
group algebra determines the group . Dealing with MIP, we investigated
a question whether the nilpotency class of a finite -group is determined by
its modular group algebra over the field of elements. We give a positive
answer to this question provided one of the following conditions holds: (i)
; (ii) \cl(G)=2; (iii) is cyclic; (iv) is a group of
maximal class and contains an abelian subgroup of index .Comment: 8 page
Formality theorems for Hochschild complexes and their applications
We give a popular introduction to formality theorems for Hochschild complexes
and their applications. We review some of the recent results and prove that the
truncated Hochschild cochain complex of a polynomial algebra is non-formal.Comment: Submitted to proceedings of Poisson 200
A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces
It is well-known that a Severi-Brauer surface has a rational point if and
only if it is isomorphic to the projective plane. Given a Severi-Brauer
surface, we study the problem to decide whether such an isomorphism to the
projective plane, or such a rational point, does exist; and to construct such
an isomorphism or such a point in the affirmative case. We give an algorithm
using Lie algebra techniques. The algorithm has been implemented in Magma.Comment: 16 pages some minor revision
The tangent complex of K-theory
We prove that the tangent complex of K-theory, in terms of (abelian)
deformation problems over a characteristic 0 field k, is cyclic homology (over
k). This equivalence is compatible with the -operations. In
particular, the relative algebraic K-theory functor fully determines the
absolute cyclic homology over any field k of characteristic 0.
We also show that the Loday-Quillen-Tsygan generalized trace comes as the
tangent morphism of the canonical map .
The proof builds on results of Goodwillie, using Wodzicki's excision for
cyclic homology and formal deformation theory \`a la Lurie-Pridham.Comment: 36 pages. Final version. To appear in Journal de l'\'Ecole
Polytechniqu
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