Geodesic
Involutions in algebras of upper-triangular matrices
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 11-30

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In this paper we classify up to equivalency involutions of first kind in algebras of upper-triangular matrices over commutative rings. In case of a field $F$ of characteristics $2$ we obtain necessary and sufficient conditions for finiteness of the set of invlolutions equivalency classes of $T_{n}(F)$.
Keywords: involution, equivalency of invloutions, algebra of upper-triangular matrices. 
@article{IVM_2023_6_a1,
     author = {I. A. Kulguskin and D. T. Tapkin},
     title = {Involutions in algebras of upper-triangular matrices},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {11--30},
     publisher = {mathdoc},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_6_a1/}
}
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I. A. Kulguskin; D. T. Tapkin. Involutions in algebras of upper-triangular matrices. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 11-30. http://geodesic.mathdoc.fr/item/IVM_2023_6_a1/