2,063 research outputs found
Some two-step and three-step nilpotent Lie groups with small automorphism groups
We construct examples of two-step and three-step nilpotent Lie groups whose
automorphism groups are `small' in the sense of either not having a dense orbit
for the action on the Lie group, or being nilpotent (the latter being
stronger). From the results we get also new examples of compact manifolds
covered by two-step simply connected Lie groups, which do not admit Anosov
automorphisms.Comment: 14 page
Continued fraction expansions for complex numbers - a general approach
We introduce here a general framework for studying continued fraction
expansions for complex numbers and establish some results on the convergence of
the corresponding sequence of convergents. For continued fraction expansions
with partial quotients in a discrete subring of an analogue of the
classical Lagrange theorem, characterising quadratic surds as numbers with
eventually periodic continued fraction expansions, is proved. Monotonicity and
exponential growth are established for the absolute values of the denominators
of the convergents for a class of continued fraction algorithms with partial
quotients in the ring of Eisenstein integers.Comment: 15 page
On the embeddability of certain infinitely divisible probability measures on Lie groups
We describe certain sufficient conditions for an infinitely divisible
probability measure on a class of connected Lie groups to be embeddable in a
continuous one-parameter convolution semigroup of probability measures.
(Theorem 1.3). This enables us in particular to conclude the embeddability of
all infinitely divisible probability measures on certain Lie groups, including
the so called Walnut group (Corollary 1.5). The embeddability is concluded also
under certain other conditions (Corollary 1.4 and Theorem 1.6).Comment: 24 page
Multi-dimensional metric approximation by primitive points
We refine metrical statements in the style of the Khintchine-Groshev Theorem
by requiring certain coprimality constraints on the coordinates of the integer
solutions
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