1,452 research outputs found
f
We introduce the notion of fq-derivation as a new derivation of G-algebra. For an endomorphism map f of any G-algebra X, we show that at least one fq-derivation of X exists. Moreover, for such a map, we show that a self-map dqf of X is fq-derivation of X if X is an associative medial G-algebra. For a medial G-algebra X, dqf is fq-derivation of X if dqf is an outside fq-derivation of X. Finally, we show that if f is the identity endomorphism of X then the composition of two fq-derivations of X is a fq-derivation. Moreover, we give a condition to get a commutative composition
Gradings of non-graded Hamiltonian Lie algebras
A thin Lie algebra is a Lie algebra graded over the positive integers
satisfying a certain narrowness condition. We describe several cyclic grading
of the modular Hamiltonian Lie algebras H(2\colon\n;\omega_2) (of dimension
one less than a power of ) from which we construct infinite-dimensional thin
Lie algebras. In the process we provide an explicit identification of
H(2\colon\n;\omega_2) with a Block algebra. We also compute its second
cohomology group and its derivation algebra (in arbitrary prime
characteristic).Comment: 36 pages, to be published in J. Austral. Math. Soc. Ser.
Affine surfaces with trivial Makar-Limanov invariant
We study the class of 2-dimensional affine k-domains R satisfying ML(R) = k,
where k is an arbitrary field of characteristic zero. In particular, we obtain
the following result:
Let R be a localization of a polynomial ring in finitely many variables over
a field of characteristic zero. If ML(R) = K for some field K included in R and
such that R has transcendence degree 2 over K, then R is K-isomorphic to
K[X,Y,Z]/(XY-P(Z)) for some nonconstant polynomial P(Z) in K[Z].Comment: 12 pages. See also http://aix1.uottawa.ca/~ddaigle/index.htm
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