The Campbell-Hausdorff group and a polar decomposition of graded algebra automorphisms
نویسندگان
چکیده
منابع مشابه
On Marginal Automorphisms of a Group Fixing the Certain Subgroup
Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...
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چکیده ندارد.
The group of automorphisms of the algebra of one-sided inverses of a polynomial algebra, II
The algebra Sn of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting, left (but not two-sided) inverses of the canonical generators of the algebra Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of auto...
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We prove that the group of automorphisms of the Lie algebra DerK(Pn) of derivations of a polynomial algebra Pn = K[x1, . . . , xn] over a field of characteristic zero is canonically isomorphic to the the group of automorphisms of the polynomial algebra Pn.
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The classical Baker-Campbell-Hausdorff formula gives a recursive way to compute the Hausdorff series H = ln(ee ) for noncommuting X, Y . Formally H lives in the graded completion of the free Lie algebra L generated by X, Y . We present a closed explicit formula for H = ln(ee ) in a linear basis of the graded completion of the free metabelian Lie algebra L̄ = L/[[L, L], [L, L]].
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1988
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1988.131.219