Generators of simple modular Lie superalgebras

Let $X$ be one of the finite-dimensional simple graded Lie superalgebras of Cartan type $W, S, H, K, HO, KO, SHO$ or $SKO$ over an algebraically closed field of characteristic $p>3$. In this paper we prove that $X$ can be generated by one element except the ones of type $W,$ $HO$, $KO$ or $SKO$ in certain exceptional cases, in which $X$ can be generated by two elements. As a subsidiary result, we also prove that certain classical Lie superalgebras or their relatives can be generated by one or two elements

Simultaneous deformations and Poisson geometry

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity algebra, which we construct explicitly. Our machinery is based on Th. Voronov's derived bracket construction. In this paper we consider only geometric applications, including deformations of coisotropic submanifolds in Poisson manifolds, of twisted Poisson structures, and of complex structures within generalized complex geometry. These applications can not be, to our knowledge, obtained by other methods such as operad theory.Comment: 32 pages. Results in Section 2 improved (Lemma 2.6 and Corollaries 2.20, 2.22). Corollary 2.5 and Corollary 2.11 added. Final version, accepted for publicatio

Controllability of quantum mechanical systems by root space decomposition of su(N)

The controllability property of the unitary propagator of an N-level quantum mechanical system subject to a single control field is described using the structure theory of semisimple Lie algebras. Sufficient conditions are provided for the vector fields in a generic configuration as well as in a few degenerate cases.Comment: 11 pages, revtex

Building suitable sets for locally compact groups by means of continuous selections

If a discrete subset S of a topological group G with the identity 1 generates a dense subgroup of G and S \cup {1} is closed in G, then S is called a suitable set for G. We apply Michael's selection theorem to offer a direct, self-contained, purely topological proof of the result of Hofmann and Morris on the existence of suitable sets in locally compact groups. Our approach uses only elementary facts from (topological) group theory.Comment: No changes except page layout. 11 pages. To appear in: Topology and its Application

Reproductive Biology and Adaptability of the Invasive Alien Freshwater Amphipod Crangonyx floridanus (Crustacea: Amphipoda, Crangonyctidae)

We studied the reproductive biology and adaptability of the alien freshwater crangonyctid amphipod Crangonyx floridanus, currently inhabiting a large portion of Japan, both in the field and under controlled laboratory conditions. In the Chikuma River population of this alien amphipod, egg-bearing individuals were found throughout the year. In terms of egg maturation cycle, egg development (during embryogenesis), and egg count per ovipositional cycle, these amphipods display a very efficient reproductive system. This study also established their adaptability to a wide range of water temperatures (primarily 4-20 degrees C, however in some cases, these individuals are able to survive at up to 30 degrees C). C. floridanus's strong capacity to adapt to broad and variable environmental conditions is certainly contributing to its high rate of population increase, and rapid dispersion throughout Japan.ArticleZOOLOGICAL SCIENCE. 27(6):522-527 (2010)journal articl

Finite-dimensionality in Tanaka theory

In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications.Comment: In this version I extend the last section by including a description of all rank 2 and 3 distributions with infinite-dimensional symmetry algebra. The second proof of Theorem 1 for semi-strongly regular case is omitted in this version (as excessive), but it is valid/accessible through version 1

Generators of simple Lie algebras in arbitrary characteristics

In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.Comment: 26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.

Rapid expansion of the distributional range and the population genetic structure of the freshwater amphipod Crangonyx floridanus in Japan

The freshwater amphipod Crangonyx floridanus (Amphipoda: Crangonyctidae) is considered to have been recently introduced from North America to Japan, and the recorded sites at which it has been collected now cover nearly all of Japan except for the northern part. In this study, we surveyed further areas outside of its known distribution range, and examined the population genetic structure and the phylogenetic relationships between Japanese and North American populations of this species based on nuclear (18S rRNA) and mitochondrial (COI) DNA sequences. We found that this amphipod has already reached Hokkaido, northernmost Japan, which suggests that it has undergone rapid expansion in a pattern of concentric circles from the central part of Japan. Genetic analysis showed that the Japanese population is genetically homogeneous, in contrast to the genetic diversification of this species seen in North American Crangonyx populations. The process of introducing, establishing, and expanding this amphipod in Japan may be explained as follows. A limited number of individuals from a North American native population were probably inadvertently introduced and established somewhere within the Kanto region. The local population size then increased and its distribution range expanded rapidly across Japan.ArticleLIMNOLOGY. 12(1):75-82 (2011)journal articl

A single-chip 20-channel speech spectrum analyzer

金沢大学理工研究域　電子情報学