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Linear representations of regular rings and complemented modular lattices with involution
Faithful representations of regular -rings and modular complemented
lattices with involution within orthosymmetric sesquilinear spaces are studied
within the framework of Universal Algebra. In particular, the correspondence
between classes of spaces and classes of representables is analyzed; for a
class of spaces which is closed under ultraproducts and non-degenerate finite
dimensional subspaces, the latter are shown to be closed under complemented
[regular] subalgebras, homomorphic images, and ultraproducts and being
generated by those members which are associated with finite dimensional spaces.
Under natural restrictions, this is refined to a --correspondence between
the two types of classes
Geometry of quantum dynamics in infinite dimension
We develop a geometric approach to quantum mechanics based on the concept of
the Tulczyjew triple. Our approach is genuinely infinite-dimensional and
including a Lagrangian formalism in which self-adjoint (Schroedinger) operators
are obtained as Lagrangian submanifolds associated with the Lagrangian. As a
byproduct we obtain also results concerning coadjoint orbits of the unitary
group in infinite dimension, embedding of the Hilbert projective space of pure
states in the unitary group, and an approach to self-adjoint extensions of
symmetric relations.Comment: 32 page
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