The Farrell--Tate and Bredon homology for PSL_4(Z) via cell subdivisions

in Journal of Pure and Applied Algebra (2019), 223(7), 2872-2888

We provide some new computations of Farrell–Tate and Bredon (co)homology for arithmetic groups. For calculations of Farrell–Tate or Bredon homology, one needs cell complexes where cell stabilizers fix ... [more ▼]

We provide some new computations of Farrell–Tate and Bredon (co)homology for arithmetic groups. For calculations of Farrell–Tate or Bredon homology, one needs cell complexes where cell stabilizers fix their cells pointwise. We provide two algorithms computing an efficient subdivision of a complex to achieve this rigidity property. Applying these algorithms to available cell complexes for PSL_4(Z) provides computations of Farrell–Tate cohomology for small primes as well as the Bredon homology for the classifying spaces of proper actions with coefficients in the complex representation ring. [less ▲]

Describing units of integral group rings up to commensurability

in Journal of Pure and Applied Algebra (2015), 219(7), 2901--2916

We restrict the types of 2 × 2-matrix rings which can occur as simple components in the Wedderburn decomposition of the rational group algebra of a finite group. This results in a description up to ... [more ▼]

We restrict the types of 2 × 2-matrix rings which can occur as simple components in the Wedderburn decomposition of the rational group algebra of a finite group. This results in a description up to commensurability of the group of units of the integral group ring ZG for all finite groups G that do not have a non-commutative Frobenius complement as a quotient. [less ▲]

Bifix codes and interval exchanges

in Journal of Pure and Applied Algebra (2014)

Big monodromy theorem for abelian varieties over finitely generated fields

in Journal of Pure and Applied Algebra (2013), 217(2), 218--229

An abelian variety over a field K is said to have big monodromy, if the image of the Galois representation on l-torsion points, for almost all primes l contains the full symplectic group. We prove that ... [more ▼]

An abelian variety over a field K is said to have big monodromy, if the image of the Galois representation on l-torsion points, for almost all primes l contains the full symplectic group. We prove that all abelian varieties over a finitely generated field K with the endomorphism ring Z and semistable reduction of toric dimension one at a place of the base field K have big monodromy. We make no assumption on the transcendence degree or on the characteristic of K. This generalizes a recent result of Chris Hall. [less ▲]

Wheeled PROPs, graph complexes and the master equation

in Journal of Pure and Applied Algebra (2009), 213(4), 496-535

We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg ... [more ▼]

We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg free wheeled PROP whose representations are in one-to-one correspondence with formal germs of SP-manifolds, key geometric objects in the theory of Batalin–Vilkovisky quantization. We also construct minimal wheeled resolutions of classical operads Com and Ass as non-trivial extensions of the well-known dg operads Com-infinityand Ass-infinity source. Finally, we apply the above results to a computation of cohomology of a directed version of Kontsevich’s complex of ribbon graphs. [less ▲]

On a general approach to the formal cohomology of quadratic Poisson structures

in Journal of Pure and Applied Algebra (2007), 208(3), 887--904