相关论文: Magic Squares of Lie Algebras

This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.

The article surveys published and not yet published results about moduli spaces of algebraic surfaces.

This article was originally published in Topology 22 (1983). The present hyperTeXed redaction includes references to post-1983 results as Addenda, and corrects a few typographical errors. (See math.GT/0411115 for a more comprehensive…

See http://www.math.msu.edu/~abbas or Wiley preprint server.

We demonstrate the existence of $K$-multimagic squares of order $N$ consisting of distinct integers whenever $N>2 K(K+1)$. This improves upon our earlier result in which we only required $N+1$ distinct integers. Additionally, we present a…

This paper has been withdrawn owing a re-arrangement of two previously submitted papers. The new version of the theoretical work on the triaxial shape of dark matter haloes can be found at the ArXiv astro-ph list (CO) as article 1104.2905

This paper has been withdrawn since we combine this paper with math.AC/0503685. All contents of the paper have been moved to math.AC/0503685.

The results of this paper have been subsumed by those of our new paper arXiv:0910.1858

The revised version has two additional references and a shorter proof of Proposition 5.7. This version also makes numerous small changes and has an appendix containing a proof of the degree formula for a parametrized surface.

We humbly and briefly offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constants II (2019), both published by Cambridge University Press. Comments are always welcome.

Recently, the classical Freudenthal Magic Square has been extended over fields of characteristic 3 with two more rows and columns filled with (mostly simple) Lie superalgebras specific of this characteristic. This Supermagic Square will be…

The construction of Freudenthal's Magic Square, which contains the exceptional simple Lie algebras, in terms of symmetric composition algebras is further developed here. The para-Hurwitz algebras, which form a subclass of the symmetric…

We prove part of the conjectures in [Li10a] (arXiv:1007.5384). We also relate the construction of quantum modified algebras in [Li10a] with the functorial construction in [ZH08](arXiv:0803.3668).

I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.

An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.

This paper has been withdrawn by the author.

The Lie superalgebras in the extended Freudenthal Magic Square in characteristic 3 are shown to be related to some known simple Lie superalgebras, specific to this characteristic, constructed in terms of orthogonal and symplectic triple…

We show arithmetic triplets of Gaussian squares are in 3-to-1 correspondence with Pythagorean triples thereof. This correspondence would transform a solution to the Magic Square of Squares puzzle into a larger structure of perfect Gaussian…

This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) together. Please see the new version of the latter paper for the…

Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…