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Articles 1 - 8 of 8
Full-Text Articles in Algebra
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
Downloads
This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.
What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre
What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre
Tutorials on... in 1 hour or less
This Maple worksheet demonstrates the salient new features and functionalities of the 2022 release of the DifferentialGeometry software package.
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Publications
A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the …
On The Construction Of Simply Connected Solvable Lie Groups, Mark E. Fels
On The Construction Of Simply Connected Solvable Lie Groups, Mark E. Fels
Research Vignettes
This worksheet contains the implementation of Theorems 4.2, 5.4 and 5.7 in the paper On the Construction of Solvable Lie Groups. All the examples in the paper are demonstrated here, along with one in Section 6 that was too long to include in the article.
Non-Isomorphic Real Simple Lie Algebras Of The Same Complex Type And Character, Ian M. Anderson
Non-Isomorphic Real Simple Lie Algebras Of The Same Complex Type And Character, Ian M. Anderson
Tutorials on... in 1 hour or less
Complex simple Lie algebras are classified by their root types. The type of a real simple Lie algebra is the root type of the associated complex algebra. The character of a real simple Lie algebra is the signature of its Killing form.
For many root types, the character is sufficient to uniquely classify the corresponding real Lie algebras. However, one should not take this statement to be literally true – there are a few cases where the character does not suffice to distinguish all possible real forms.
In this worksheet we will show that the 2 real non-isomorphic Lie algebras …
Cartan Involutions And Cartan Decompositions Of A Semi-Simple Lie Algebra, Ian M. Anderson
Cartan Involutions And Cartan Decompositions Of A Semi-Simple Lie Algebra, Ian M. Anderson
Tutorials on... in 1 hour or less
In this worksheet we shall review the basic definitions and properties of Cartan involutions and Cartan decompositions and illustrate these using the DifferentialGeometry software package for Lie algebras.
A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson
A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson
Tutorials on... in 1 hour or less
Let I be a differential system on a manifold M. The infinitesimal symmetry algebra of I is the set of all vectors fields X on M such that preserve I. In this worksheet we present an example, due to E. Cartan of a rank 7 Pfaffian system on a 15-dimensional manifold whose infinitesimal symmetry algebra is the split real form of the exceptional Lie algebra f4 .
How To Create A Lie Algebra, Ian M. Anderson
How To Create A Lie Algebra, Ian M. Anderson
How to... in 10 minutes or less
We show how to create a Lie algebra in Maple using three of the most common approaches: matrices, vector fields and structure equations. PDF and Maple worksheets can be downloaded from the links below.