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On the tensor algebra of a non-abelian group and applications |
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| Authors: | Hans Joachim Baues and Daniel Conduché |
| Institution: | (1) Max-Planck-Institut für Mathematik, Gottfried-Claren-Str. 26, D-5300 Bonn 3, Germany;(2) Université de Rennes I, UFR de mathématiques, Campus de Beaulieu, 35042 Rennes Cedex, France |
| Abstract: | We introduce the tensor algebra J( ) of a crossed complex and give its relations with the James construction for a filtered space. For a group G, we define via multi-derivations the derived algebra I
*
G which is isomorphic to the algebra C(JG) of chains on JG We derive from a certain exact sequence for the homology H*JG applications to the homotopy of the suspended classifying space  BG. |
| Keywords: | Tensor algebra crossed tensor algebra James construction crossed complex filtered space non-Abelian tensor product classifying space |
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