THE BV-ALGEBRA STRUCTURE OF THE HOCHSCHILD COHOMOLOGY OF THE GROUP RING OF CYCLIC GROUPS OF PRIME ORDER

2016 ◽  
Author(s):  
Andrés Angel ◽  
Diego Duarte
Keyword(s):  
Group Ring ◽  
Prime Order ◽  
Hochschild Cohomology ◽  
Algebra Structure ◽  
Cyclic Groups ◽  
Bv Algebra

scholarly journals Higher Brackets on Cyclic and Negative Cyclic (Co)Homology

2018 ◽  
Vol 2020 (23) ◽  
pp. 9148-9209
Author(s):  
Domenico Fiorenza ◽  
Niels Kowalzig
Keyword(s):  
Hochschild Cohomology ◽  
Cyclic Homology ◽  
Cyclic Cohomology ◽  
Algebra Structure ◽  
String Topology ◽  
Cohomology Groups ◽  
Poincare Duality ◽  
Homology Groups ◽  
Bv Algebra ◽  
Special Case

Abstract The purpose of this article is to embed the string topology bracket developed by Chas–Sullivan and Menichi on negative cyclic cohomology groups as well as the dual bracket found by de Thanhoffer de Völcsey–Van den Bergh on negative cyclic homology groups into the global picture of a noncommutative differential (or Cartan) calculus up to homotopy on the (co)cyclic bicomplex in general, in case a certain Poincaré duality is given. For negative cyclic cohomology, this in particular leads to a Batalin–Vilkoviskiĭ (BV) algebra structure on the underlying Hochschild cohomology. In the special case in which this BV bracket vanishes, one obtains an $e_3$-algebra structure on Hochschild cohomology. The results are given in the general and unifying setting of (opposite) cyclic modules over (cyclic) operads.

scholarly journals Atomic Latin Squares based on Cyclotomic Orthomorphisms

10.37236/1919 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Ian M. Wanless
Keyword(s):  
Finite Fields ◽  
Complete Graph ◽  
Prime Order ◽  
Automorphism Groups ◽  
Latin Square ◽  
Latin Squares ◽  
Established Method ◽  
Cyclic Groups ◽  
Complete Bipartite Graphs ◽  
First Time

Atomic latin squares have indivisible structure which mimics that of the cyclic groups of prime order. They are related to perfect $1$-factorisations of complete bipartite graphs. Only one example of an atomic latin square of a composite order (namely 27) was previously known. We show that this one example can be generated by an established method of constructing latin squares using cyclotomic orthomorphisms in finite fields. The same method is used in this paper to construct atomic latin squares of composite orders 25, 49, 121, 125, 289, 361, 625, 841, 1369, 1849, 2809, 4489, 24649 and 39601. It is also used to construct many new atomic latin squares of prime order and perfect $1$-factorisations of the complete graph $K_{q+1}$ for many prime powers $q$. As a result, existence of such a factorisation is shown for the first time for $q$ in $\big\{$529, 2809, 4489, 6889, 11449, 11881, 15625, 22201, 24389, 24649, 26569, 29929, 32041, 38809, 44521, 50653, 51529, 52441, 63001, 72361, 76729, 78125, 79507, 103823, 148877, 161051, 205379, 226981, 300763, 357911, 371293, 493039, 571787$\big\}$. We show that latin squares built by the 'orthomorphism method' have large automorphism groups and we discuss conditions under which different orthomorphisms produce isomorphic latin squares. We also introduce an invariant called the train of a latin square, which proves to be useful for distinguishing non-isomorphic examples.

ON THE DENSITY OF DISCRIMINANTS OF ABELIAN EXTENSIONS OF A NUMBER FIELD

2010 ◽  
Vol 06 (06) ◽  
pp. 1273-1291
Author(s):  
BEHAILU MAMMO
Keyword(s):  
Asymptotic Formula ◽  
Galois Group ◽  
Number Field ◽  
Algebraic Number ◽  
Prime Order ◽  
Algebraic Number Field ◽  
Abelian Extensions ◽  
Cyclic Groups

Let G = Cℓ × Cℓ denote the product of two cyclic groups of prime order ℓ, and let k be an algebraic number field. Let N(k, G, m) denote the number of abelian extensions K of k with Galois group G(K/k) isomorphic to G, and the relative discriminant 𝒟(K/k) of norm equal to m. In this paper, we derive an asymptotic formula for ∑m≤XN(k, G; m). This extends the result previously obtained by Datskovsky and Mammo.

scholarly journals HIGHER INDICATORS FOR SOME GROUPS AND THEIR DOUBLES

2012 ◽  
Vol 11 (02) ◽  
pp. 1250030 ◽  
Author(s):  
MARC KEILBERG
Keyword(s):  
Semidirect Product ◽  
Prime Order ◽  
Abelian Groups ◽  
Dihedral Groups ◽  
Cyclic Groups ◽  
Generalized Quaternion ◽  
Drinfel'd Doubles

In this paper we explicitly determine all indicators for groups isomorphic to the semidirect product of two cyclic groups by an automorphism of prime order, as well as the generalized quaternion groups. We then compute the indicators for the Drinfel'd doubles of these groups. This first family of groups include the dihedral groups, the non-abelian groups of order pq, and the semidihedral groups. We find that the indicators are all integers, with negative integers being possible in the first family only under certain specific conditions.

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