单结合环的切代数的多项式恒等式
Polynomial identities for tangent algebras of monoassociative loops
AI总结：
本文通过引入n次Sabinin代数并利用交换子、结合子与四元子的多项式恒等式刻画4次情形，构造了满足单结合性a^2 a = a a^2的解析环切空间上的自然代数结构，并给出一个不能由低次恒等式推出的5次恒等式。
摘要：
我们引入n次Sabinin代数，它由Sabinin代数中次数不超过n的多项式恒等式所定义。4次Sabinin代数可以通过自由非结合代数中交换子、结合子以及两个四元子所满足的多项式恒等式来刻画。我们在自由幂结合代数中考虑这些运算，并证明其中一个四元子是多余的。所得代数给出了解析环在单位元处切空间上的自然结构，对于该解析环，所有局部环都满足单结合性 a^2 a = a a^2。这些代数是超越李代数、Malcev代数和Bol代数的下一步。我们还给出一个5次恒等式，它被这三个运算所满足，但不能由更低次的恒等式推出。
英文摘要：
We introduce degree n Sabinin algebras, which are defined by the polynomial identities up to degree n in a Sabinin algebra. Degree 4 Sabinin algebras can be characterized by the polynomial identities satisfied by the commutator, associator and two quaternators in the free nonassociative algebra. We consider these operations in a free power associative algebra and show that one of the quaternators is redundant. The resulting algebras provide the natural structure on the tangent space at the identity element of an analytic loop for which all local loops satisfy monoassociativity, a^2 a = a a^2. These algebras are the next step beyond Lie, Malcev, and Bol algebras. We also present an identity of degree 5 which is satisfied by these three operations but which is not implied by the identities of lower degree.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
