Quaternionic homology of the tensor algebra T(V)
by
Eduardo Quiñónez-Rico
New Mexico State University

For a quaternionic module Q_* its quaternionic homology HQ(M_*) may be defined in terms of Tor functors. For the sake of calculations an explicit resolution of the trivial k^f-module is provided. The program of constructing such a resolution consists of ensambling resolutions of k over K[Q_n] . Even though when a 4-periodic resolution can be used, another resolution is provided instead. The construcion of this resolution is achieved by using Wall's construction applied to the extension

Z → Qm → Z/2 → 0

An example of a quaternionic module is given by the modules A^⊕n, where A is a k-algebra with involution. A computation for the tensor algebra A=T(V) is provided, yielding

HQ(T(V)) = H*(Pin(2), Z) ⊕ å m ≥ 1  H*(Qm, Vm)

This result is analogous to the cyclic and dihedral cases given by J.-L. Loday and J. Lodder.

Date received: February 18, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caak-50.