2020 Fiscal Year Final Research Report
a generalization of the notion of a module for a vertex algebra
| Project/Area Number |
18K03198
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Review Section |
Basic Section 11010:Algebra-related
|
|---|
| Research Institution | Hokkaido University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2018-04-01 – 2021-03-31
|
| Keywords | 頂点代数 |
|---|
| Outline of Final Research Achievements |
The vertex algebra associated to a non-degenerate even lattice, and its invariant subalgebra, plays an important role in constructing vertex algebras with good properties. If the lattice is positive definite, the modules for a vertex algebra are well studied, but if not, we need to deal with a broader class of representations called weak modules. The author classified the irreducible weak modules for an invariant subalgebra of the vertex algebra associated to a non-degenerate even lattice. The author also showed that every weak module for the same vertex algera is completely reducible.
|
| Free Research Field |
代数学
|
| Academic Significance and Societal Importance of the Research Achievements |
頂点代数上の弱加群は，格子に付随する頂点代数の表現に現れる自然な対象である．ムーンシャイン頂点作用素代数の性質の解明に重要な役割を果たすと考えているが，通常の加群における手法が全く使えなくなるため，弱加群を研究することはこれまで極めて困難であった．筆者は頂点代数の特性を活かした，表現を調べる新しい手法を導入し，不変部分代数の表現論を進展させた．
|
