相关论文: Magic Squares of Lie Algebras
The authors of this article intend to present some results obtained in the study of biderivations of complete Lie algebras. Firstly they present a matricial approach to do this, which was a useful and explanatory tool not only in the study…
We give a unified description of morphisms and comorphisms of Lie pseudoalgebras, showing that the both types of morphisms can be regarded as subalgebras of a Lie pseudoalgebra, called the $\psi$-sum. We also provide similar descriptions…
The original version of this paper contains an error; when this is corrected the basic conclusion changes. A revised manuscript will be submitted shortly.
This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2073.
The purpose of this paper is to introduce the notion of isoclinism and cover in a multiplicative Lie algebra which may be helpful to describe all multiplicative Lie algebra structures on a group. Consequently, we give the existence of the…
This paper has been withdrawn due to an error in one of the equations in the extended portion.
In these notes we provide the foundation for the deformation theoretic parts of arXiv:0807.3753 and arXiv:math/0102005.
This is a preprint version of a chapter for Handbook of Algebra.
We present all real solvable algebraically rigid Lie algebras of dimension $n\leq 8$. The difference between the classification of complex and real rigid Lie algebras is analyzed.
This paper has been withdrawn, as it is superseded by arXiv:0806.2122 (Bloch-Kato exponential maps for local fields with imperfect residue fields), which is a more recent version of the same paper.
The original version of this paper has been withdrawn by the authors and merged with the revised version of astro-ph/9702014.
This is an overview article on Lie algebroids, and their role as the infinitesimal counterparts of Lie groupoids.
In this comment we show that the approach presented by Foj\'on et al~\cite{Fojon10} is not as accurate as they claim. A straightforward calculation using the models considered buy those authors clearly shows that the spectral method, which…
This paper has been withdrawn. The contents of this paper can now be found in 0907.3000, which combines the erstwhile 0901.2981 and 0901.2982 in a somewhat compact form.
This is a short communication in reference to the comments in (arXiv: 1605.05147) of our paper in Int. J. Mod. Phys. D 25, 1650051 (2016). We have tried to answer to the comments or criticism in the paper.
Pre-publication version withdrawn at the request of the journal. Final version now available in Reviews of Particle Physics at http://pdg.lbl.gov/2004/reviews/contents_sports.html
This paper continues math.GR/0608302's study of amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and applies it to graded algebras associated with finitely generated groups. Due to a…
We give an introduction to the structure theory of extended affine Lie algebras, which provide a common framework for finite-dimensional semisimple, affine and toroidal Lie algebras. The notes are based on a lecture series given during the…
A working mathematician's summary of many results on the derived category, perverse sheaves, and vanishing cycles. This is the August 2025 version, with a completely revised section on vanishing cycles.
This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850