Related papers: On the dimension of the sheets of a reductive Lie …

We address two errors made in our paper arXiv:1511.03423. The most significant error is in Theorem 1.1. We repair this error, and show that the main result, Theorem 2.5 of arXiv:1511.03423, is true. The second error is in one of our…

This is the original version of my Ph.D. thesis. The main results have been divided up between papers arXiv:2111.09784 and arXiv:2204.10924. This paper has been kept on the arXiv to preserve some proofs of elementary lemmas that will be…

An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.

We revisit the third fundamental theorem of Lie (Lie III) for finite dimensional Lie algebras in the context of infinite dimensional matrices.

In the Letter 'Comment on 'Affine density, von Neumann dimension and a problem of Perelomov', arXiv.2211.04879, by Prof. J. L. Romero, it is claimed that the main theorem of Ref2 := [Adv. Math. 407, Article ID 108564, 22 p. (2022)] is…

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

The helping Lemma 7 in [Maslowski and Wijsen, ICDT, 2014] is false. The lemma is used in (and only in) the proof of Theorem 3 of that same paper. In this corrigendum, we provide a new proof for the latter theorem.

It is shown that a recent article by Z.-D. Zhang [arXiv:0705.1045] is in error and violates well-known theorems.

Theorem 7 in Ref. [Linear Algebra Appl., 430, 1-6, (2009)] states sufficient conditions to determine whether a pair generates the algebra of 3x3 matrices over an algebraically closed field of characteristic zero. In that case, an explicit…

As recently pointed out by Gabe, a fundamental paper by Elliott and Kucerovsky concerning the absorption theory for C*-algebras contains an error, and as a consequence we must report that Lemma 4.5 in "Classifying C*-algebras with both…

Restricted Lie algebras of dimension up to $3$ over algebraically closed fields of positive characteristic were classified by Wang and his collaborators in [25, 19]. In this paper, we obtain a classification of restricted Lie algebras of…

We point out that the main theorem of Ref2 := [Adv. Math. 407, Article ID 108564, 22 p. (2022)] is included in the prior research survey Ref1 := [Expo. Math., 40(2), 265-301, 2022]. For context, we also reproduce the rather simple proof…

It is shown that criticism of my paper arXiv:0801.0656 Phys. Rev. Lett, vol. 101, 163202 (2008) by the authors of Comment arXiv:0810.3243v1 is wrong and that their main arguments are in contradiction with established concepts of statistical…

The property 4 in Proposition 2.3 from the paper "Some remarks on Davie's uniqueness theorem" is replaced with a weaker assertion which is sufficient for the proof of the main results. Technical details and improvements are given.

The present preprint completes the arXiv preprint #2202.11652, entitled "Pseudodifferential arithmetic and the Riemann hypothesis", devoted to a proof of the conjecture. The first 4 pages of that preprint were devoted to a set of necessary…

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

This version of the paper corrects an inaccuracy in the proof of Theorem 2.9 in the published version. The main results remain unchanged.

It is shown that the arguments in the reply of Z.-D. Zhang (arXiv:0812.0194) to the comment arXiv:0811.1802 defending his conjectures in arXiv:0705.1045 are invalid. His conjectures have been thoroughly disproved.

We study Lie subalgebras $L$ of the vector fields $\mathrm{Vec}^{c}({\mathbb A}^{2})$ of affine 2-space ${\mathbb A}^{2}$ of constant divergence, and we classify those $L$ which are isomorphic to the Lie algebra $\mathfrak{aff}_{2}$ of the…

Transposed Poisson $3$-Lie algebra is a dual notion of Nambu-Poisson algebra of order 3. In this paper, we explicitly determine all $\frac{1}{3}$-derivations and automorphisms of the unique nontrivial $3$-dimensional complex $3$-Lie algebra…