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Lie. varvalis / varvelis
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Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Given a (quasi-)twilled pre-Lie algebra, we first construct a differential graded Lie algebra ([Formula: see text]-algebra). Then we study the twisting theory of (quasi-)twilled pr...
Categorification of $ \mathsf{VB} $-Lie algebroids and $ \mathsf{VB} $-Courant algebroids
Categorification of $ \mathsf{VB} $-Lie algebroids and $ \mathsf{VB} $-Courant algebroids
<abstract><p>In this paper, first we introduce the notion of a $ \mathsf{VB} $-Lie $ 2 $-algebroid, which can be viewed as the categorification of a $ \mathsf{VB} $-L...
LIE -HIGHER DERIVATIONS AND LIE -HIGHER DERIVABLE MAPPINGS
LIE -HIGHER DERIVATIONS AND LIE -HIGHER DERIVABLE MAPPINGS
Let ${\mathcal{A}}$ be a unital torsion-free algebra over a unital commutative ring ${\mathcal{R}}$. To characterise Lie $n$-higher derivations on ${\mathcal{A}}$, we give an ident...
3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras
3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras
In this paper, we first introduce the notion of a 3-Hom–Lie bialgebra and give an equivalent description of the 3-Hom–Lie bialgebras, the matched pairs and the Manin triples of 3-H...
Coherent categorical structures for Lie bialgebras, Manin triples, classical r-matrices and pre-Lie algebras
Coherent categorical structures for Lie bialgebras, Manin triples, classical r-matrices and pre-Lie algebras
Abstract
The broadly applied notions of Lie bialgebras, Manin triples, classical r-matrices and
...
On the Lie triple derivation of Hom–Lie superalgebras
On the Lie triple derivation of Hom–Lie superalgebras
Consider a Hom–Lie superalgebra, denoted by [Formula: see text]. In this paper, we inquire the Lie triple derivation [Formula: see text] and generalized Lie triple derivation [Form...
3-Lie∞-algebras and 3-Lie 2-algebras
3-Lie∞-algebras and 3-Lie 2-algebras
In this paper, we introduce the notions of a [Formula: see text]-[Formula: see text]-algebra and a 3-Lie 2-algebra. The former is a model for a 3-Lie algebra that satisfy the funda...
Robust navigation for industrial service robots
Robust navigation for industrial service robots
Robust, reliable and safe navigation is one of the fundamental problems of robotics. Throughout the present thesis, we tackle the problem of navigation for robotic industrial mobil...