Projective Space: Lines and Duality
We offer an axiomatic presentation of three-dimensional projective space that adopts the line as its fundamental element and renders automatic the principle of duality.
math.CO↗
arXiv subjects
P. L. Robinson
Publications and source records attributed to P. L. Robinson.
Cayley-Sylvester invariants and the Hamilton equations
We note implications of the Cayley-Sylvester theory of invariants and covariants for the Hamilton equations generated by cubic and quartic Hamiltonian functions.
math.SG↗
Cubic Hamiltonians
We determine a precise necessary and sufficient condition for completeness of the Hamiltonian vector field associated to a homogeneous cubic polynomial on a symplectic plane.
math.SG↗
Automorphisms of Quadratic Liouville Structures
We examine the diffeomorphisms of a symplectic vector space that preserve a chosen symplectic potential. Our examination yields an explicit description of these diffeomorphisms when the chosen potential differs from the canonical potential by the differential of a homogeneous quadratic in one of three broad classes.
math.SG↗
Automorphisms of Liouville Structures
By a Liouville structure on a symplectic manifold $(M, ω)$ we mean a choice of symplectic potential: that is, a choice of one-form $θ$ on $M$ such that ${\rm d} θ= ω$. We determine precisely all the automorphisms of a Liouville structure in case $(M, ω)$ is a symplectic vector space and $θ$ differs from its canonical symplectic potential by the differential of a homogeneous monomial.
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Distributive Quotients
We note that each lattice $L$ has a unique largest distributive quotient, of which every distributive quotient of $L$ is itself a quotient.
math.RA↗
'Twisted duality' in the ${\rm C^*}$ Clifford algebra
Let $V$ be a real inner product space and $C[V]$ its ${\rm C}^*$ Clifford algebra. We prove that if $Z$ is a subspace of $V$ then $C[Z^{\perp}]$ coincides with the supercommutant of $C[Z]$ in $C[V]$.
math.RA↗
'Twisted duality' for Clifford Algebras
Viewing the complex Clifford algebra $C(V)$ of a real inner product space $V$ as a superalgebra, we offer several proofs of the fact that if $W$ is a subspace of the complexification of $V$ then the supercommutant of the Clifford algebra $C(W)$ is precisely the Clifford algebra $C(W^{\perp})$.
math.RA↗
Correctness of depiction in planar diagrams of spatial figures
We show that it is possible to decide whether a given planar diagram correctly depicts the spatial figure consisting of a planar quadrangle together with its shadow in another plane.
math.GM↗
Bosonic kernels
We show that the bosonic Fock representation of a complex Hilbert space admits a purely algebraic kernel calculus; as an illustration, we use it to reproduce the standard integral kernel formulae for metaplectic operators within the complex-wave representation.
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Creator-annihilator domains and the number operator
We show that for the bosonic Fock representation in infinite dimensions, the maximal common domain of all creators and annihilators properly contains the domain of the square-root of the number operator.
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The bosonic Fock representation and a generalized Shale theorem
We detail a new approach to the bosonic Fock representation of a complex Hilbert space V: our account places the bosonic Fock space S[V] between the symmetric algebra SV and its full antidual SV'; in addition to providing a context in which arbitrary (not necessarily restricted) real symplectic automorphisms of V are implemented, it offers simplified proofs of many standard results of the theory.
math.FA↗