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Abstract Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms, and the generalized analysis method and concise kinematics transfer matrix are obtained. In this study, f...

In this work we obtain all rigid complex 3-dimensional multiplicative Hom-Lie algebras. This is done by studying all deformations of multiplicative Hom-Lie algebras which are also Lie algebras. As a byproduct, we obtain ...

This paper extends the classification of three-dimensional connected topological proper loops , for which the multiplication group  is a six-dimensional decomposable solvable Lie group. Building upon the significant res...

We call the p-fundamental string of a complex simple Lie algebra to the sequence of irreducible representations having highest weights of the form kω1 +ωp for k ≥ 0, where ωj denotes the jth fundamental weight of th...

An exactly solvable quantum many-fermion system with an arbitrarily strong two-body interaction is studied and some exact thermodynamic functions (in the thermodynamic limit) are derived within the framework of the stati...

We generalize a result on the Heisenberg Lie algebra that gives restrictions to possible Lie bialgebra cobrackets on 2-step nilpotent algebras with some additional properties. For the class of 2-step nilpotent Lie algebr...

In this paper we describe all the nilradicals of parabolic subalgebras of split real simple Lie algebras admitting symplectic structures.The main tools used to obtain this list are Kostant's description of the highest we...

We establish the conjugacy of Cartan subalgebras for extended affine Lie algebras whose centreless core is “of type A”, i.e., ℓ×ℓ-matrices over a quantum torus Q whose trace lies in the commutator space of Q. Th...

We study homological properties of a family of algebras called toupie algebras. Our main objective is to obtain the Gerstenhaber structure of their Hochschild cohomology, with the purpose of describing the Lie algebra st...

We study left invariant conformal Killing–Yano (CKY) 2-forms on Lie groups endowed with a left invariant metric. We classify all 5-dimensional metric Lie algebras carrying CKY tensors that are obtained as a one-dimensi...

We construct many examples of Lie groups admitting a left-invariant metric of negative Ricci curvature. We study Lie algebras which are semidirect products l= (a⊕ u) ⋉ n and we obtain examples where u is any semisimp...

We show that the definition of unrolled Hopf algebras can be naturally extended to the Nichols algebra B(V) of a Yetter-Drinfeld module V on which a Lie algebra g acts by biderivations. As a special case, we find unrolle...

In this article we present some probably unexpected (in our opinion) properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra...

We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformatio...

Abstract Topology and performance are the two main topics dealt in the development of robotic mechanisms. However, it is still a challenge to connect them by integrating the modeling and design process of both parts in a...

This paper studies a Lie group extension of the generalized-α time integration method for the simulation of flexible multibody systems. The equations of motion are formulated as an index-3 differential-algebraic equatio...

The main objectives of the study are to develop a new adaptive geometric method for real-time monitoring of industrial electricity consumption schedules to ensure timely detection of structural imbalances and minimizatio...

Let M be a compact Riemannian manifold and let μ,d be the associated measure and distance on M. Robert McCann, generalizing results for the Euclidean case by Yann Brenier, obtained the polar factorization of Borel maps ...

In two-dimensional models of critical non-intersecting loops, there are $\ell$-leg fields that insert $\ell∈\mathbb{N}^*$ open loop segments, and diagonal fields that change the weights of closed loops. We conjecture a...

Let Gr be a component of the Grassmann manifold of a C*-algebra, presented as the unitary orbit of a given orthogonal projection Gr=Gr(P). There are several natural connections on this manifold, and we first show that th...