A polynomial approach to cocycles over elementary abelian groups∗
نویسنده
چکیده
We derive bivariate polynomial formulae for cocycles and coboundaries in Z(Zp , Zp ), and a basis for the (p − 1 − n)-dimensional GF (p)-space of coboundaries. When p = 2we determine a basis for the (2+ ( n 2 ) −1)-dimensional GF (2)-space of cocycles and show each cocycle has a unique decomposition as a direct sum of a coboundary and a multiplicative cocycle of restricted form.
منابع مشابه
Cocycles over Abelian Tns Actions
We study extensions of higher-rank abelian TNS actions (i.e. hyperbolic and with a special structure of the stable distributions) by compact connected Lie groups. We show that up to a constant, there are only finitely many cohomology classes. We also show the existence of cocycles over higher-rank abelian TNS actions that are not cohomologous to constant cocycles. This is in contrast to earlier...
متن کاملComputing Resolutions Over Finite p-Groups
A uniform and constructive approach for the computation of resolutions and for (co)homology computations for any finite p-group is detailed. The resolutions we construct ([32]) are, as vector spaces, as small as the minimal resolution of IFp over the elementary abelian p-group of the same order as the group under study. Our implementations are based on the development of sophisticated algebraic...
متن کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
متن کاملDUAL HOPF ORDERS IN GROUP RINGS OF ELEMENTARY ABELIAN p-GROUPS
Let R be the valuation ring ofK, a finite extension of Qp containing a primitive pth root of unity, and let G be an elementary abelian p-group of order p, with dual group Ĝ. We construct a new family of triangular Hopf orders over R in KG, a proper subfamily whose duals are also triangular, and a proper subfamily of that family whose construction extends the truncated exponential construction o...
متن کاملAn Elementary Classification of Symmetric 2-Cocycles
We present a classification of the so-called “additive symmetric 2-cocycles” of arbitrary degree and dimension over Zp, along with a partial result and some conjectures for m-cocycles over Zp, m > 2. This expands greatly on a result originally due to Lazard and more recently investigated by Ando, Hopkins, and Strickland, which together with their work culminates in a complete classification of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012