Search results for "FINE"

Equivariant Triviality of Quasi-Monomial Triangular $$\mathbb{G}_{a}$$-Actions on $$\mathbb{A}^{4}$$

2014

We give a direct and self-contained proof of the fact that additive group actions on affine four-space generated by certain types of triangular derivations are translations whenever they are proper. The argument, which is based on explicit techniques, provides an illustration of the difficulties encountered and an introduction to the more abstract methods which were used recently by the authors to solve the general triangular case.

Language Recognition Power and Succinctness of Affine Automata

2016

In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by Diaz-Caro and Yakaryilmaz [6] referred as affine automata. First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which allows us to characterize the class of exclusive stochastic languages. Then, we initiate a study on the succintness of affine automata. In particular, we show that an infinite family of unary regular languages can be recognized by 2-state affine automata, whereas the number of states of any quantum and probabilistic automata cannot be bounded. Finally, we present the characterization …

A Vector Approach to Euler's Line of a Triangle

1992

Among the many interesting properties that triangles possess there is one that quickly attracts our curiosity and stays easily in our mind: The centroid, circumcentre and orthocentre all lie in a common line (Euler's Line). An elementary simple proof can be obtained using metric and affine properties of the points involved, [1]. Our aim here is to illustrate a proof using vectors. We identify points in the plane with their position vectors. It is easy to see that the centroid G of the triangle ABC is given by the identity

Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac

1991

We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.

Non-integrality of the PI-exponent of special Lie algebras

2013

If L is a special Lie algebra over a field of characteristic zero, its sequence of codimensions is exponentially bounded. The PI-exponent measures the exponential rate of growth of such sequence and here we give a first example of a special Lie algebra whose (upper and lower) PI-exponent is non-integer.

On the Codimension Growth of Finite-Dimensional Lie Algebras

1999

Abstract We study the exponential growth of the codimensions cn(L) of a finite-dimensional Lie algebra L over a field of characteristic zero. We show that if the solvable radical of L is nilpotent then lim n → ∞ c n ( L ) exists and is an integer.

Some criteria for detecting capable Lie algebras

2013

Abstract In virtue of a recent bound obtained in [P. Niroomand, F.G. Russo, A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra 39 (2011) 1293–1297], we classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one. Indirectly, we find also a criterion for detecting noncapable Lie algebras. The final part contains a construction, which shows that there exist capable Lie algebras of arbitrary big corank (in the sense of Berkovich–Zhou).

Irreducible Finitary Lie Algebras over Fields of Characteristic Zero

1998

Abstract A Lie subalgebraLof g l K (V) is said to befinitaryif it consists of elements of finite rank. We show that if Char  K  = 0, if dim K  Vis infinite, and ifLacts irreducibly onV, then the derived algebra ofLis simple.

General measure theory

1995

A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms

2017

Abstract The realification of the ( 2 n + 1 ) -dimensional complex Heisenberg Lie algebra is a ( 4 n + 2 ) -dimensional real nilpotent Lie algebra with a 2-dimensional commutator ideal coinciding with the centre, and admitting the compact algebra sp ( n ) of derivations. We investigate, in general, whether a real nilpotent Lie algebra with 2-dimensional commutator ideal coinciding with the centre admits a compact Lie algebra of derivations. This also gives us the occasion to revisit a series of classic results, with the expressed aim of attracting the interest of a broader audience.