紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2017, 54(3), p. 533-568

LIE ALGEBRAS CONSTRUCTED WITH LIE MODULES AND THEIR POSITIVELY AND NEGATIVELY GRADED MODULES

Sasano, Nagatoshi

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2017-07

In this paper, we shall give a way to construct a graded Lie algebra L(g,ρ,V,ν,Bₒ) from a standard pentad (g,ρ,V,ν,Bₒ) which consists of a Lie algebra gg which has a non-degenerate invariant bilinear form Bₒ and g-modules (ρ,V) and ν⊂ Hom(V, F) all defined over a field F with characteristic 0. In general, we do not assume that these objects are finite-dimensional. We can embed the objects g,ρ,V,ν into L(g,ρ,V,ν,Bₒ). Moreover, we construct specific positively and negatively graded modules of L(g,ρ,V,ν,Bₒ). Finally, we give a chain rule on the embedding rules of standard pentads.

10.18910/66999

66999

LIE ALGEBRAS CONSTRUCTED WITH LIE MODULES AND THEIR POSITIVELY AND NEGATIVELY GRADED MODULES

Sasano, Nagatoshi

Osaka University and Osaka City University, Departments of Mathematics

英語

2017-07

Osaka Journal of Mathematics

54

3

533

568

https://hdl.handle.net/11094/66999

10.18910/66999

https://doi.org/10.18910/66999