We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
On Connection between Second-Degree Exterior and Symmetric Derivations of Kähler Modules.
- Authors
Merkepçi, Hamiyet
- Abstract
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) .
- Subjects
MATHEMATICAL physics; DIFFERENTIAL equations; ADIABATIC invariants; BOUNDARY value problems; MATHEMATICAL symmetry
- Publication
Symmetry (20738994), 2018, Vol 10, Issue 9, p365
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym10090365