On $N$-differential graded algebras

Differential graded Lie groups and their differential graded Lie algebras

In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to differential graded Lie groups (DGLG). We first recall the classical problem of integration in the context, and present the construction for (non-graded) differential Lie algebras. Then, we define the category of differential graded Lie groups and study its properties. We show how to associate a differential graded Lie algebra to every differential graded Lie group and vice-versa. For the DGLA $\to$ DGLG direction, the main ``tools'' are graded Hopf algebras and Harish-Chandra pairs (HCP) -- we defi…

On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this …

Differential geometry of the Z_3-graded quantum superplane

In this work, differential geometry of the Z$_3$-graded quantum superplane is constructed. The corresponding quantum Lie superalgebra and its Hopf algebra structure are obtained.

关于与伪H型李代数相关的共形伪次黎曼基本分次李代数

On conformal pseudo-subriemannian fundamental graded Lie algebras associated with pseudo $H$-type Lie algebras

本文研究由伪H型李代数自然产生的共形伪次黎曼基本分次李代数，证明在特定假设下其延长与相应基本分次李代数的延长一致。

Conformal pseudo-subriemannian fundamental graded Lie algebras of semisimple type

We introduce the notion of a conformal pseudo-subriemannian fundamental graded Lie algebra of semisimple type. Moreover we give a classification of conformal pseudo-subriemannian fundamental graded Lie algebras of semisimple type and their prolongations.

分次斜Clifford代数的光滑几何

Smooth geometry of graded skew Clifford algebras

该论文聚焦分次斜Clifford代数领域，针对其微分光滑性展开研究，属于代数与微分几何交叉方向的理论探索。