A case study of quantization of curves surfaces: The Myllar balloon
A complex from linear elasticity
Introduction: This article will present just one example of a general construction known as the Bernstein-Gelfand-Gelfand (BGG) resolution. It was the motivating example from two lectures on the BGG resolution given at the 19th Czech Winter School on Geometry and Physics held in Srní in January 1999. This article may be seen as a technical example to go with a more elementary introduction which will appear elsewhere [M. Eastwood, Notices Am. Math. Soc. 46, No. 11, 1368-1376 (1999)]. In fact, there...
A construction of finite-dimensional faithful representation of Lie algebra
Summary: The Ado theorem is a fundamental fact, which has a reputation of being a `strange theorem'. We give its natural proof.
A gauge theory for the Kadomtsev-Petviashvili system
A generalization of Fueter’s monogenic functions to fine domains
A generalized Leibniz rule and foundation of a discrete quaternionic analysis
A high-order helicity invariant and the Rokhlin theorem
A note on Fiedler-Moravek combinatorial problem
A note on n-ary Poisson brackets
An -ary Poisson bracket (or generalized Poisson bracket) on the manifold is a skew-symmetric -linear bracket of functions which is a derivation in each argument and satisfies the generalized Jacobi identity of order , i.e.,
A problem about Feynman integrals on Riemannian manifolds
A quaternionic treatment of Navier-Stokes equations
A remark on natural quantum Lagrangians and natural generalized Schrödinger operators in Galilei quantum mechanics
A remark on the -splitting conjecture
A remark on the topology of higher order frames
A representation of the coalgebra of derivations for smooth spaces
Let be a field. The generalized Leibniz rule for higher derivations suggests the definition of a coalgebra for any positive integer . This is spanned over by , and has comultiplication and counit defined by and (Kronecker’s delta) for any . This note presents a representation of the coalgebra by using smooth spaces and a procedure of microlocalization. The author gives an interpretation of this result following the principles of the quantum theory of geometric spaces.
A survey of boundary value problems for bundles over complex spaces
Let be a reduced -dimensional complex space, for which the set of singularities consists of finitely many points. If denotes the set of smooth points, the author considers a holomorphic vector bundle , equipped with a Hermitian metric , where represents a closed analytic subset of complex codimension at least two. The results, surveyed in this paper, provide criteria for holomorphic extension of across , or across the singular points of if . The approach taken here is via the metric...
A unified construction of the Alexander- and the Jones-invariant
A vector lattice variant of the ergodic theorem
About duality and Killing tensors
Summary: In this paper the isometries of the dual space were investigated. The dual structural equations of a Killing tensor of order two were found. The general results are applied to the case of the flat space.
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