Related papers: Magic Squares of Lie Algebras

This results in this paper have been merged with the result in arXiv:1003.0167. The authors would like to withdraw this version. Please see arXiv:1008.5356 for the merged version.

This is a corrected version of our paper published in Osaka Journal of Mathematics 51(2014), 673-693. We correct Theorem~1.1, Proposition~3.3 and their proofs.

In this paper, the author gives two methods to construct complete Lie algebras. Both methods show that the derivation algebras of some Lie algebras are complete.

This paper is withdrawn due to a mistake. The revised version with a new tiltle can be found in hep-ph/0502199.

These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.

We find the numbers of $3 \times 3$ magic, semimagic, and magilatin squares, as functions either of the magic sum or of an upper bound on the entries in the square. Our results on magic and semimagic squares differ from previous ones in…

This article contains the last part of the mini-course `Spaces: a perspective view' delivered at the IFWGP2012. Here I deal with the part of the mini-course which centers on the classification questions associated to the simple real Lie…

The results are still valid, however this letter is superceeded by a significantly extended version which is available at astro-ph/0003358 and is scheduled for publication in the ApJ Dec. 10, 2000. We have withdrawn this letter to avoid…

A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.

This paper has been withdrawn because the models on which it was based have undergone significant changes and improvements. A new paper with the same title, based on the improved models, is accepted for publication in MNRAS and is available…

This paper is intended to help the readers to understand the article: Y. Hirashita, Least-Squares Prices of Games, Preprint (arXiv:math.OC/0703079).

This paper has been withdrawn by the authors, because it has been made obsolete by the detailed expositions in our papers in arXiv:0812.4885 (the mathematics part) and arXiv:0812.4737 (the economics part).

The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.

In this paper, we study the classical and pre-Lie Magnus expansions, discussing how we can find a recursion for the pre-Lie case which already incorporates the pre-Lie identity. We give a combinatorial vision of a numerical method proposed…

This paper has been withdrawn because it is a duplicate of [math/0609208].

The present paper is mainly a survey of our work arXiv:0708.4221 and arXiv:0808.2440 but it also contains the announcement of some new results. Its main purpose is to present an accessible introduction to a technique allowing efficient…

Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…

This paper has been withdrawn by the author(s), due to the existence of a much better paper in http://arxiv.org/abs/cs.CR/0207027

The paper is withdrawn and will be replaced at a later time by a significantly revised and extended version.

Paper erroneously re-submitted as duplicte. Readers should look at math-ph/9909004.