Results 21 to 30 of about 215 (48)
An algebraic framework of weighted directed graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 58, Page 3657-3678, 2003., 2003 We show that an algebraic formulation of weighted directed graphs leads to introducing a k‐vector space equipped with two coproducts Δ and Δ˜ verifying the so‐called coassociativity breaking equation (Δ˜⊗id)Δ=(id⊗Δ)Δ˜. Such a space is called an L‐coalgebra.
Philippe Leroux
wiley +1 more source
A NeutroStructural Framework for Coordinated Development Evaluation of Land Resource Utilization and Ecological Environmental Protection [PDF]
Neutrosophic Sets and SystemsBalancing land resource utilization with ecological environmental protection has become a global necessity in the face of accelerating urbanization, agriculture expansion, and climate change.
Qian Luan
doaj +1 more source
Graded manifolds and Drinfeld doubles for Lie bialgebroids [PDF]
, 2002 We define \textit{graded manifolds} as a version of supermanifolds endowed with an additional $\mathbb Z$-grading in the structure sheaf, called \textit{weight} (not linked with parity).
Voronov, Theodore
core +4 more sources
A generalised hopf algebra for solitons
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 12, Page 701-718, 2002., 2002 This paper considers a generalisation of the idea of a Hopf algebra in which a commutative ring replaces the field in the unit and counit. It is motivated by an example from the inverse scattering formalism for solitons. We begin with the corresponding idea for groups, where the concept of the identity is altered.
Falleh R. Al-Solamy, Edwin J. Beggs
wiley +1 more source
Noncommutative Symmetries and Gravity [PDF]
, 2006 Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms.
Abe E +20 more
core +5 more sources
Bicovariant Quantum Algebras and Quantum Lie Algebras [PDF]
, 1992 A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from \fun\ to \uqg\ , given by elements of the pure braid group.
B. Drabant +20 more
core +2 more sources
Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited)
Neutrosophic Sets and Systems, 2020 In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that ...
openaire +2 more sources
The Hopf Algebra Structure of the Character Rings of Classical Groups [PDF]
, 2012 The character ring \CGL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra \Sym$ of symmetric functions.
Fauser, Bertfried +2 more
core +1 more source
Universal central extensions of Hom-Lie antialgebras
, 2019 We develop a theory of universal central extensions for Hom-Lie antialgebra. It is proved that a Hom-Lie antialgebra admits a universal central extension if and only if it is perfect. Moreover, we show that the kernel of the universal central extension is equal to the second homology group with trivial coefficients.
Zhang, Tao, Zhong, Deshou
openaire +2 more sources
Noncommutative Geometry and Gravity
, 2005 We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product.
Aschieri, Paolo +3 more
core +2 more sources