Related papers: An introduction to Lie group integrators -- basics…
We show how Langevin diffusions can be interpreted in the context of stochastic Hamiltonian systems with structure-preserving noise and dissipation on reductive Lie groups. Reductive Lie groups provide the setting in which the Lie group…
A Lie system is the non-autonomous system of differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional Lie algebra of vector fields, a so-called Vessiot--Guldberg Lie…
We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical…
Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…
We investigate coherency properties of certain completed integral group rings, precisely for compact $p$-adic Lie groups.
We define and analyse the properties of contact Lie systems, namely systems of first-order differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of…
In this paper we prove isomorphisms between 5 Lie groups (of arbitrary dimension and fixed signatures) in Clifford algebra and classical matrix Lie groups - symplectic, orthogonal and linear groups. Also we obtain isomorphisms of…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…
In this book, I explored differential equations for operation in Lie group and for representations of group Lie in a vector space.
We develop a semi-discrete version of discrete variational mechanics with applications to numerical integration of classical field theories. The geometric preservation properties are studied.
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants.…
This is a concise introduction to the theory of Lie groupoids, with emphasis in their role as models for stacks. After some preliminaries, we review the foundations on Lie groupoids, and we carefully study equivalences and proper groupoids.…
It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive, cocomplete, symmetric, closed, monoidal…
We provide a motivated introduction to the theory of categorical actions of groups and the local geometric Langlands program. Along the way we emphasize applications, old and new, to the usual representation theory of reductive and affine…
We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients…
In this paper, we introduce local expressions for discrete Mechanics. To apply our results simultaneously to several interesting cases, we derive these local expressions in the framework of Lie groupoids, following the program proposed by…
Integration of polynomials over the classical groups of unitary, orthogonal and symplectic matrices can be reduced to basic building blocks known as Weingarten functions. We present an elementary derivation of these functions.
The first aim of this paper is to show that any finite-dimensional reductive Lie algebra and its finite-dimensional completely reducible representation can be embedded into some PC Lie algebra. The second aim is to find the structure of a…
We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the…