The Freiheitssatz and automorphisms for 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.

Keywords:

• Automorphism
• brace algebra
• Freiheitssatz
• word problem

AMS Mathematics Subject Classification (2010):

• 17A30
• 17A50
• 17A36
• 17D25

Acknowledgments

The authors would like to thank the anonymous referee for helpful comments.

Additional information

Funding

Supported by the NNSF of China (11501237, 11401246), the NSF of Guangdong Province of China (2016A030310099), the Outstanding Young Teacher Training Program in Guangdong Universities (YQ2015155), the Characteristic Innovation Project of Guangdong Provincial Department of Education (2017KTSCX173), the Science and Technology Program of Huizhou City (2016X0429044, 2017C0404020), and the Huizhou University (hzu201804, hzu201704, hzuxl201523).