Lie-like Algebras (Superalgeras)
We introduce the notion of a Lie-like algebra$^{\diamond}$ (superalgebra$^{\diamond}$) for $\diamond\in\{^{1-st}, ^{2-nd}, ^{3-rd} \}$.
math.RA↗
arXiv subjects
Keqin Liu
Publications and source records attributed to Keqin Liu.
Generalized Cohn's Theorem
We introduce the notion of a free associative $\mathcal{Z}_2$-algebra on the union of two disjoint sets and prove a generalization of Cohn's Theorem on Jordan algebras.
math.RA↗
New Generalizations of Poisson Algebras
We introduce many new generalizations of Poisson algebras which can be constructed inside the associative algebra of linear transformations over a vector space.
math.RA↗
Extended Hilbert's Nullstellensatz
We prove the extended Hilbert's Nullstellensatz in the context of Hu-Liu polynomial trirings.
math.AG↗
Even (Odd) Roots and Simple Leibniz Algebras with Lie Factor $s\ell_2$
We introduce 3-irreducible modules, even roots and odd roots for Leibniz algebras, produce a basis for a root space of a Leibniz algebra with a semisimple Lie factor, and classify finite dimensional simple Leibniz algebras with Lie factor $s\ell_2$.
math.RA↗
Generalizations of Jordan Algebras and Malcev Algebras
We introduce two classes of nonassociative algebras and define the building blocks in the context of the new nonassociative algebras.
math.RA↗
Number-Like Objects and the Extended Lie Correspondence
We classify finite dimensional division real associative $\mathcal{Z}_2$-algebras, introduce composition $\mathcal{Z}_2$-algebras, and extend the Campbell-Baker-Hausdorff series and Lie correspondence in the context of linear Hu-Liu Leibniz algebras.
math.RA↗
$ξ$-Groups and Hu-Liu Leibniz Algebras
We initiate the study of $ξ$-groups and Hu-Liu Leibniz algebras, claim that alomost all simple Leibniz algebras and simple Hu-Liu Leibniz algebras are linear, and establish two passages. One is the passage from a special $\mathcal{Z}_2$-graded associative algebra to a Hu-Liu Leibniz algebra. The other one is the passage from a linear $ξ$-group to its tangent space which is a Hu-Liu Leibniz algebra.
math.RA↗
Lying-Over Theorem on Left Commutative Rngs
We introduce the notion of a graded integral element, prove the counterpart of the lying-over theorem on commutative algebra in the context of left commutative rngs, and use the Hu-Liu product to select a class of noncommutative rings.
math.AC↗
Tangent-like Spaces to Local Monoids
The main new notions are the notions of tangent-like spaces and local monoids. The main result is the pasage from a local monoid to its tangent-like space which is a local Leibniz algebra.
math.RA↗
How to Expand the Zariski Topology
We introduce the notion of a Hu-Liu prime ideal in the context of left commutative rngs, and establish the contravariant functor from the category of left commutative rngs into the category of topological spaces.
math.RA↗
A Class of Ring-like Objects
We introduce the notions of one-sided dirings, 3-irreducible left modules, 3-primitive left dirings, 3-semi-primitive left dirings, 3-primitive ideals and 3-radicals. The main results consists of two parts. The first part establishes two external characterizations of a 3-semi-primitive left diring. The second part characterizes the 3-radical of a left diring by using 3-primitive ideals.
math.RA↗
Transformation Digroups
We introduce the notion of a transformation digroup and prove that every digroup is isomorphic to a transformation digroup.
math.GR↗
A class of group-like object
We introduce a class of group-like objects and prove that Cayley Theorem on groups has a counterpart in the class of group-like objects.
math.RA↗