The algebra of constraints arising in the canonical quantization of N=1 supergravity in four dimensions is investigated. Using the holomophic action it is shown that the algebra does not close formally.

the famous primary and cyclic decomposition theorems along with the tightly related rational and jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.

This article presents a natural extension of the tensor algebra. This extended algebra is based on a vector space as the ordinary tensor algebra is. In addition to “left multiplications” by vectors, we can consider “derivations” by covectors as fundamental operators on this algebra. These two types of operators satisfy an analogue of the canonical commutation relations, and we can regard the al...

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

In this paper we have studied the nature of kinematical and dynamical laws in κ-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of κ-Minkowski phase space algebra that yields the κ-extended finite Lorentz transformations derived in [16]. This is a particular form of a Deformed Special Relativity model that admits a modified energy-mom...

In this paper we have studied the nature of kinematical and dynamical laws in κ-Minkowski spacetime from a new perspective: the canonical phase space approach. We have introduced a new form of κ-Minkowski phase space algebra from which we recover the κ-extended finite Lorentz transformations derived in [13]. This is a particular form of a Deformed Special Relativity model that admits a modified...

We further develop the theory of inducing W -graphs worked out by Howlett and Yin (Math. Z. 244(2):415–431, 2003 and Manuscr. Math. 115(4):495– 511, 2004), focusing on the case W = Sn. Our main application is to give two W -graph versions of tensoring with the Sn defining representation V , one being H ⊗HJ − for H ,HJ the Hecke algebras of Sn,Sn−1 and the other ( ̂ H +⊗H −)1, where ̂ H + is a sub...

The famous primary and cyclic decomposition theorems along with the tightly related rational and Jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.