The L-algebra of Hurwitz primes

JOURNAL OF NUMBER THEORY

卷:190

Article

Rump, Wolfgang¹ 

[1] Univ Stuttgart, Inst Algebra & Number Theory, Pfaffenwaldring 57, D-70550 Stuttgart, Germany

关键词: Hurwitz prime;    Metacommutation;    L-algebra;    Right l-group;    Garside group;   

DOI  :  10.1016/j.jnt.2018.03.004

来源: Elsevier

【 摘 要 】

Conway and Smith proved that up to recombination of conjugate primes and migration of units, the only obstruction to unique factorization in the ring of Hurwitz integers in the quaternions is metacommutation of primes with distinct norm. We show that the Hurwitz primes form a discrete L*-algebra, a quantum structure which provides a general explanation for metacommutation. L-algebras arise in the theory of Artin-Tits groups, quantum logic, and in connection with solutions of the quantum Yang-Baxter equation. It is proved that every discrete L*-algebra admits a natural embedding into a right l-group, which yields a new class of Garside groups. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free