Physical Sciences and Mathematics Commons^™

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

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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

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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

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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 .

Polynomials Occuring In Generating Function Identities For B-Ary Partitions, David Dakota Blair

Graduate Student Publications and Research

Let p_b(n) be the number of integer partitions of n whose parts are powers of b. For each m there is a generating function identity:

f_m(b,q)\sum_{n} p_b(n) q^n = (1-q)^m \sum_{n} p_b(b^m n q)q^n

where n ranges over all integer values. The proof of this identity appears in the doctoral thesis of the author. For more information see http://dakota.tensen.net/2015/rp/.

This dataset is a JSON object with keys m from 1 to 23 whose values are f_m(b,q).