Journal of the Ramanujan Mathematical Society

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Cohesively Related Pairs of Extensions of Sheaves of Lie Algebras


Affiliations
1 Department of Mathematics, Seethalakshmi Ramaswami College, Tiruchirapalli, Tamil Nadu, India
2 Department of Mathematics, Bharathidasan University, Tiruchirapalli, Tamil Nadu, India
     

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A Characterisation of the pair of extensions over sheaves G1 and G2 of R-Lie Algebras, with abelian kernel A, which arise from an extension of the product sheaf G1 © G2 with the same abelian kernel A, is brought out. It is shown that the set C (G1 G2; A) of all equivalence classes of Cohesively related pairs of extensions forms an abelian group, which is a homomorphic image of H2 (G1, G2;A).

Keywords

Locally Trivial Extension, Cohesively Related Pairs of Extensions, Almost Central Local Splitting Extensions.
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  • Cohesively Related Pairs of Extensions of Sheaves of Lie Algebras

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Authors

Leela Devi
Department of Mathematics, Seethalakshmi Ramaswami College, Tiruchirapalli, Tamil Nadu, India
N. Ramabhadran
Department of Mathematics, Bharathidasan University, Tiruchirapalli, Tamil Nadu, India

Abstract


A Characterisation of the pair of extensions over sheaves G1 and G2 of R-Lie Algebras, with abelian kernel A, which arise from an extension of the product sheaf G1 © G2 with the same abelian kernel A, is brought out. It is shown that the set C (G1 G2; A) of all equivalence classes of Cohesively related pairs of extensions forms an abelian group, which is a homomorphic image of H2 (G1, G2;A).

Keywords


Locally Trivial Extension, Cohesively Related Pairs of Extensions, Almost Central Local Splitting Extensions.