We introduce anyonic Lie algebras in terms of structure constants. We provide the simplest examples and formulate some open problems.

The observed large-scale scatter in Lyman $\alpha$ opacity of the intergalactic medium at $z<6$ implies large fluctuations neutral hydrogen fraction that are unexpected long after reionization has ended. A number models have emerged to explain these make testable predictions for relationship between Ly$\alpha$ and density. We present selections $z=5.7$ Ly$\alpha$-emitting galaxies (LAEs) fields...

We show that the spectral fluctuations of the two-body random ensemble exhibit 1/f noise. This result supports a recent conjecture stating that chaotic quantum systems are characterized by 1/f noise in their energy level fluctuations. After suitable individual averaging, we also study the distribution of the exponent alpha in the 1/ f(alpha) noise for the individual members of the ensemble. Alm...

Blending methods of Topological Dynamics and Control Theory, we develop a new technique to construct compact-Lie-group-valued minimal cocycles arising as fundamental matrix solutions of linear diierential equations with recurrent coeecients subject to a given constraint. The precise requirement on the coee-cients is that they belong to a speciied closed convex subset S of the Lie algebra L of t...

In this paper we describe the derivations of orthosymplectic Lie superalgebras over a superring. In particular, we derive sufficient conditions under which the derivations can be expressed as a semidirect product of inner and outer derivations. We then present some examples for which these conditions hold.

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group G, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition in simple factors of these Lie algebras, in terms of the ordinary representations of G. MSC 2000 : 20C15,17B99.

A well known theorem of Duflo, the “annihilation theorem”, claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is centrally generated. For the Lie superalgebra osp(1, 2l), this result does not hold. In this article, we introduce a “correct” analogue of the centre for which the annihilation theorem does hold in the case osp(1, 2l). This sub...

An initial-boundary value problem of subdiffusion type is considered; the temporal component differential operator has form $$\sum _{i=1}^{\ell }q_i(t)\, D _t ^{\alpha _i} u(x,t)$$ , where $$q_i$$ are continuous functions, each $$D _i}$$ a Caputo derivative, and $$\alpha _i$$ lie in (0, 1]. Maximum/comparison principles for this proved under weak hypotheses. A new positivity result multinomial ...