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The Farrell--Tate and Bredon homology for PSL_4(Z) via cell subdivisions ; Rahm, Alexander ; 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 ▲] Detailed reference viewed: 165 (15 UL)The mod 2 cohomology rings of SL_2 of the imaginary quadratic integers Rahm, Alexander ; in Journal of Pure and Applied Algebra (2016), 220 Detailed reference viewed: 53 (2 UL)The finite index basis property ; ; et al in Journal of Pure and Applied Algebra (2015) We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems ... [more ▼] We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namely the class of tree sets. We prove as a main result that for a uniformly recurrent tree set S, a finite bifix code X on the alphabet A is S-maximal of S-degree d if and only if it is the basis of a subgroup of index d of the free group on A [less ▲] Detailed reference viewed: 75 (4 UL)The homotopy theory of bialgebras over pairs of operads Yalin, Sinan in Journal of Pure and Applied Algebra (2014), 218(6), 973-991 We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic ... [more ▼] We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in two steps. In the first step, we equip coalgebras over an operad with a cofibrantly generated model category structure. In the second step we use the adjunction between bialgebras and coalgebras via the free algebra functor. This result allows us to do classical homotopical algebra in various categories such as associative bialgebras, Lie bialgebras or Poisson bialgebras in chain complexes. [less ▲] Detailed reference viewed: 58 (0 UL)Bifix codes and interval exchanges ; ; et al in Journal of Pure and Applied Algebra (2014) Detailed reference viewed: 70 (1 UL)Big monodromy theorem for abelian varieties over finitely generated fields Arias De Reyna Dominguez, Sara ; ; 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 ▲] Detailed reference viewed: 73 (0 UL)The integral homology of $ PSL_2$ of imaginary quadratic integers with nontrivial class group Rahm, Alexander ; in Journal of Pure and Applied Algebra (2011), 215(6), 1443--1472 Detailed reference viewed: 57 (22 UL)Wheeled PROPs, graph complexes and the master equation ; Merkulov, Sergei ; 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 ▲] Detailed reference viewed: 94 (2 UL)Equivalences of Higher Derived Brackets ; Schatz, Florian in Journal of Pure and Applied Algebra (2008), 212(11), 2450-2460 This note elaborates on Th. Voronov’s construction of L-infinity-structures via higher derived brackets with a Maurer–Cartan element. It is shown that gauge equivalent Maurer–Cartan elements induce L ... [more ▼] This note elaborates on Th. Voronov’s construction of L-infinity-structures via higher derived brackets with a Maurer–Cartan element. It is shown that gauge equivalent Maurer–Cartan elements induce L-infinity-isomorphic structures. Applications in symplectic, Poisson and Dirac geometry are discussed. [less ▲] Detailed reference viewed: 91 (0 UL)On a general approach to the formal cohomology of quadratic Poisson structures ; Poncin, Norbert in Journal of Pure and Applied Algebra (2007), 208(3), 887--904 Detailed reference viewed: 76 (0 UL) |
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