Shtukar U
The purpose of the article is to describe all 3-dimensional subalgebras and all corresponding reductive pairs of Lie algebra of all 2 × 2 real matrices. This Lie algebra is 4-dimensional as a vector space, it’s not simple, and it’s not solvable. The evaluation procedure utilizes the canonical bases for subspaces that were introduced. In Part I of this article, all 3-dimensional subalgebras of the given Lie algebra g are classified. All reductive pairs {h, m} with 3-dimensional subalgebras h are found in Part II. Surprisingly, there is only one reductive pair {h, m} with special 3-dimensional subalgebra h and 1-dimensional complement m. Finally, all reductive pairs {h, m} with 1-dimensional subalgebras h of algebra g are classified in Part III of the article.
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