Project: ExteriorExtensions

• Potential advisor/consultant(s): Luke Oeding
• Goal: Implement a particular kind of extension of a Lie algebra inside M2
• Current status: beta testing / looking for suggestions and feedback
• Macaulay2 skill level: Intermediate+
• Mathematical experience: Grad
• Reason(s) to participate: I'm hoping to submit this package + writeup to JSAG sometime soon. Contributions / comments welcome.

Project Description

Builds a graded algebra that equivariantly extends the Lie algebra sl_n via the non-zero graded piece of the exterior algebra by defining the bracket products. Constructs matrix representations of adjoint operators. Computes ranks of blocks coming from the grading.

Examples

Examples are embedded in the file ExteriorExtensions.m2 File is available at https://github.com/LukeOeding/ExteriorExtensions.m2

References (that describe the math and/or algorithms)

Jordan Decompositions of Tensors: https://arxiv.org/abs/2206.13662