The Freiheitssatz and automorphisms for free brace algebras
Yu Li, Qiuhui Mo, Xiangui Zhao
TL;DR
This paper establishes fundamental algebraic properties of free brace algebras over fields of characteristic zero, including the Freiheitssatz, decidability of the word problem, freeness of subalgebras, and tameness of automorphisms.
Contribution
It proves the Freiheitssatz, decidability of the word problem, and tameness of automorphisms for free brace algebras, advancing understanding of their algebraic structure.
Findings
Freiheitssatz holds for free brace algebras
Word problem is decidable for single relation
Automorphisms are tame in two-generated free brace algebras
Abstract
Over a field of characteristic zero, we prove that the Freiheitssatz holds for brace algebras, the word problem for the brace algebras with a single defining relation is decidable, two generated subalgebras of free brace algebras are free, and that automorphisms of two generated free brace algebras are tame.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models