# Adjoint representation of the graded Lie algebra osp(2/1; C) and its exponentiation

Source: [Adjoint representation of the graded Lie algebra osp(2/1; C) and its exponentiation](<https://www.sota2.com/research/paper/68fa1f417a2b558e29328414>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T17:43:57.100Z

Authors: K. Ilyenko

Published: 2003-08-01T16:54:13.000Z

## Abstract

We construct explicitly the grade star Hermitian adjoint representation of osp(2/1; C) graded Lie algebra. Its proper Lie subalgebra, the even part of the graded Lie algebra osp(2/1; C), is given by su(2) compact Lie algebra. The Baker-Campbell-Hausdorff formula is considered and reality conditions for the Grassman-odd transformation parameters, which multiply the pair of odd generators of the graded Lie algebra, are clarified.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-th/0308009>)

[PDF](<https://arxiv.org/pdf/hep-th/0308009.pdf>)