A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Characterizing Algebraic Invariants by Differential Radical Invariants
[chapter]

2014
*
Lecture Notes in Computer Science
*

The

doi:10.1007/978-3-642-54862-8_19
fatcat:5fbanhbgzvbk3meu6m2luoqhg4
*characterization*leads to a*differential**radical**invariant*proof rule that is sound and complete, which implies that*invariance*of*algebraic*equations over real-closed fields is decidable. ... This so-called*differential**radical**characterization*relies on a sound abstraction of the reachable set of solutions*by*the smallest variety that contains it. ... Checking*Invariant*Varieties*by**Differential**Radical**Invariants*(Section 3.1) The*differential**radical**characterization*allows to check for and falsify the*invariance*of a variety candidate. ...##
###
Casimir operators of Lie algebras with a nilpotent radical
[article]

2007
*
arXiv
*
pre-print

We show that a Lie

arXiv:0710.0070v1
fatcat:iosb5stogjcahe7gymn2aykywq
*algebra*having a nilpotent*radical*has a fundamental set of*invariants*consisting of Casimir operators. ... We give a different proof of this fact in the special and well-known case where the*radical*is abelian. ... Since L has a nilpotent*radical*, we may assume*by*Lemma 1 that it is*algebraic*. It has therefore a fundamental set of*invariants*that consists of rational*invariants*,*by*Lemma 2. ...##
###
Algebraic Solutions to the Hamilton-Jacobi Equation with the Time-Varying Hamiltonian

2013
*
SICE Journal of Control Measurement and System Integration
*

If such an ideal is found, an

doi:10.9746/jcmsi.6.28
fatcat:24a3judwfvhptlkqoar5f66pcm
*algebraic*gradient can be obtained simply*by*solving a set of*algebraic*equations. ... In this paper, the HJE with coefficients belonging to meromorphic functions is considered, and its solutions with*algebraic*gradients are*characterized*in terms of commutative*algebra*. ... If an H-*invariant*and involutive zero-dimensional*radical*ideal is found, an*algebraic*gradient is obtained simply*by*solving a set of*algebraic*equations. ...##
###
On Computing Linearizing Coordinates From Symmetry Algebra
[article]

2020
*
arXiv
*
pre-print

A

arXiv:1810.12334v2
fatcat:mzou2m74jbgefayshxukyx2cuy
*characterization*of the symmetry*algebra*of the nth order ordinary*differential*equations (ODEs) with maximal symmetry and all third order linearizable ODEs is given. ... The procedure is illustrated*by*several examples from literature. ... These conditions*characterize*the*algebras*and the*differential*equations -intrinsically. Theorem 4.1. ...##
###
Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations
[chapter]

2014
*
Lecture Notes in Computer Science
*

The procedure is based on a necessary and sufficient condition that

doi:10.1007/978-3-319-10936-7_10
fatcat:ytgh7vnw2zhslhkgawp3chonbi
*characterizes**invariant*conjunctions of polynomial equalities. ... The procedure is based on a necessary and sufficient condition that*characterizes**invariant*conjunctions of polynomial equalities. ... The contributions of this paper are twofold: • It extends*differential**radical**invariants*[14] to obtain a*characterization*of*invariance*for*algebraic*sets under the flow of*algebraic**differential*equations ...##
###
Page 2469 of Mathematical Reviews Vol. , Issue 91E
[page]

1991
*
Mathematical Reviews
*

In particular, it is shown that the

*radical*topological groups G of finite rank can be*characterized**by*means of the lattice L(G) of all closed subgroups of G. ... A further application of the Abel transform is that it intertwines*invariant**differential*operators on G/K and Weyl group*invariant**differential*operators on A with constant coefficients. ...##
###
Page 2837 of Mathematical Reviews Vol. , Issue 83h
[page]

1983
*
Mathematical Reviews
*

Finally, R denotes the Jacobson

*radical*of Alg 2. A*characterization*of the*radical*® of a nest*algebra*as an intersection of larger ideals (the diagonal ideals) has been given*by*J. R. ... J. 21 (1971/72), 887-906; MR 45 #2516], say that an*algebra*of operators is para-refiexive if every operator which leaves*invariant*all of the algebra’s*invariant*operator ranges is in the*algebra*. ...##
###
Page 471 of Mathematical Reviews Vol. , Issue 81B
[page]

1981
*
Mathematical Reviews
*

system is

*characterized**by*its tangent Lie triple*algebra*. ... This method is a generalisation of a well- known procedure for Lie*algebras*, whose Casimir*invariants*can be found*by*solving systems of first-order linear partial*differential*equations. ...##
###
Page 6234 of Mathematical Reviews Vol. , Issue 90K
[page]

1990
*
Mathematical Reviews
*

He also gives a unified module-theoretic

*characterization*of supernilpotent*radicals*and special*radicals*. ... The main aim of the author is to motivate and introduce the notion of a quasitriangular Hopf*algebra*. This notion was first introduced*by*...##
###
Page 1272 of Mathematical Reviews Vol. 57, Issue 4
[page]

1979
*
Mathematical Reviews
*

Another result is that if M is any such class, then the upper

*radical*a defined*by*M (which is a special*radical*) is a dual supernilpotent*radical*and b=a* is a dual subidempotent*radical*with a and b ... The author presents a*characterization*of “homogeneous systems” induced on an*algebra*A in a manner analogous to the classical construction of the Lie*algebra*of A. ...##
###
Page 6874 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

The author shows that the subspace of vari- ational functions of the above space is

*characterized**by*a simple*algebraic*condition, namely, the condition of smoothnes of a sys- tem in the derivative variables ... This Darboux transformation is*characterized**by*the fact that it connects solutions of two distinct equations. ...##
###
Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators

2009
*
Journal of Physics A: Mathematical and Theoretical
*

Such operators are said to generate a virtual copy of s in U(g), and allow to compute the Casimir operators of g in closed form, using the classical formulae for the

doi:10.1088/1751-8113/42/6/065205
fatcat:yaytpfkcu5c35aavi5duocsqau
*invariants*of s. ... Given a semidirect product g=sr of semisimple Lie*algebras*s and solvable*algebras*r, we construct polynomial operators in the enveloping*algebra*U(g) of g that commute with r and transform like the generators ... left-*invariant*1-forms on the simply connected Lie group whose*algebra*is isomorphic to g allows to define an exterior*differential*d on g **by*dω (X i , X j ) = −C k ij ω (X k ) , ω ∈ g * . (5) This coboundary ...##
###
Localization and ideal theory in iterated differential operator rings

1987
*
Journal of Algebra
*

In this paper we study primahty, hypercentrality, simplicity, and localization and the second layer condition in skew enveloping

doi:10.1016/0021-8693(87)90003-2
fatcat:apnvtse3bveejeldl5dp7uriai
*algebras*and iterated*differential*operator rings. ...*algebra*R#U(L) satisfies the second layer condition. ... We can now*characterize*the prime*radical*of R# U(L). Note that if R has the a.c.c. on ideals and N is the prime*radical*of R, then N, = (N : L). ...##
###
Page 631 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 54, Issue 7
[page]

1948
*
American Mathematical Society. Bulletin of the American Mathematical Society
*

Kolchin: Existence theorems connected with the Picard- Vessiot theory of homogeneous linear ordinary

*differential*equations. It is shown how a theorem on*algebraic**differential*equations due to J. F. ... Soc. vol. 48 (1940) pp. 543-544) yields two results concerning the*differential*equation L(y)=y+pryy*")+ --- +pay=0 (f1,---, fa in an ordinary*differential*field F of charactgristic 0 with*algebraically*...##
###
Page 500 of Mathematical Reviews Vol. , Issue 85b
[page]

1985
*
Mathematical Reviews
*

Lohmus (Tartu)
18 CATEGORY THEORY, HOMOLOGICAL

*ALGEBRA*See also 01098, 18010. 85b:18001 Proceedings of the workshop held in Aarhus, June 1-15, 1983. Edited*by*A. Kock. ... Let G be a Lie*algebra*over a field k and let G* be its dual space. Suppose that the number of independent polynomial*invariants*of the coadjoint action K of G in G* is equal to the index of G [J. ...
« Previous

*Showing results 1 — 15 out of 10,457 results*