A remark on a formula of Zassenhaus

✍ Scribed by Hans Scheerer; Klaus Schuch

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 113 KB
• Volume: 39
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00182296

✦ Synopsis

Using the decomposition principle in groups of coalgebra morphisms we give a simple proof of a theorem of H. J. Baues related to an identity of Zassenhaus in algebras of prime characteristic p > 0.

The authors of [2] did not relate their method to the original identity of Zassenhaus ([3, §6]) in algebras of prime characteristic p > 0. Doing so we obtain a simple proof of a theorem of H. J. Baues ([-1,1.4.9]) without a restriction on the characteristic. In [11 this result was proved by means of homotopy theory for p >~ 3.

We will work in the setting of graded algebra as adopted in I-2] (in fact, all objects will be evenly graded).

Let R be a unitary commutative ring. Let r ~> 2, let Tz (Xl,..., x~) be the free associative algebra in generators xl,...,x, of degree 2 over Z and let Lz (xt,...,x,) be the Lie subalgebra of Tz(xl ..... x,) (considered as Lie algebra) generated by x 1 ..... xr.