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Open AccessArticle

On Connection between Second-Degree Exterior and Symmetric Derivations of Kähler Modules

Department of Mathematics, Gaziantep University, Gaziantep 27310, Turkey
Symmetry 2018, 10(9), 365; https://doi.org/10.3390/sym10090365
Received: 22 July 2018 / Revised: 17 August 2018 / Accepted: 24 August 2018 / Published: 27 August 2018
(This article belongs to the Special Issue Mathematical Physics and Symmetry)
Mathematical physics looks for ways to apply mathematical ideas to problems in physics. In differential forms, the tensor form is first defined, and the definitions of exterior and symmetric differential forms are made accordingly. For instance, M is an R-module, M R M the tensor product of M with itself and H a submodule of M R M generated by x y y x , where x , y in M. Then, 2 ( M ) = M R M / H is called the second symmetric power of M. A role of the exterior differential forms in field theory is related to the conservation laws for physical fields, etc. In this study, I present a new approach to emphasize the properties of second exterior and symmetric derivations on Kahler modules, and I find a connection between them. I constitute exact sequences of 2 ( Ω 1 ( S ) ) and Λ 2 ( Ω 1 ( S ) ) , and I describe and prove a new isomorphism in the following: Let S be an affine algebra presented by R / I , where R = k [ x 1 , x s ] is a polynomial algebra and I = ( f 1 , f m ) an ideal of R. Then, I have J 1 Ω 1 ( S ) Ω 1 ( S ) 2 ( Ω 1 ( S ) ) Λ 2 ( Ω 1 ( S ) . View Full-Text
Keywords: universal module; differential operators; Kähler module; symmetric derivation; exterior derivation universal module; differential operators; Kähler module; symmetric derivation; exterior derivation
MDPI and ACS Style

Merkepçi, H. On Connection between Second-Degree Exterior and Symmetric Derivations of Kähler Modules. Symmetry 2018, 10, 365.

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