✦ LIBER ✦

Universal central extensions of precrossed modules and Milnor's relative K2

✍ Scribed by D. Arias; M. Ladra; A. R.-Grandjeán

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 333 KB
Volume: 184
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(03)00065-3

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✦ Synopsis

We characterize the universal central extension of a perfect precrossed module giving two descriptions, one in terms of non-abelian tensor products of groups and other in terms of projective presentations. As application to relative algebraic K-theory, we obtain that Milnor's absolute and relative K2 groups are the kernel of the universal central extension of the precrossed module determined by the groups of the elementary matrices of a ring and relative to an ideal, respectively.