Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rota-Baxter operators on unital algebras   We state that all Rota-Baxter operators of nonzero weight on Grassmann
algebra over a field of characteristic zero are projections on a subalgebra
along another one. We show the one-to-one correspondence between the solutions
of associative Yang-Baxter equation and Rota-Baxter operators of weight zero on
the matrix algebra $M_n(F)$ (joint with P. Kolesnikov). We prove that all
Rota-Baxter operators of weight zero on a unital associative (alternative,
Jordan) algebraic algebra over a field of characteristic zero are nilpotent.
For an algebra $A$, we introduce its new invariant the rb-index
$\mathrm{rb}(A)$ as the nilpotency index for Rota-Baxter operators of weight
zero on $A$. We show that $\mathrm{rb}(M_n(F)) = 2n-1$ provided that
characteristic of $F$ is zero.

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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
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The categories of this paper are: stat
1
The categories of this paper are: cs