TY - JOUR

T1 - Automorphisms of the endomorphism semigroup of a free associative algebra

AU - Belov-Kanel, A.

AU - Berzins, A.

AU - Lipyanski, R.

PY - 2007

Y1 - 2007

N2 - Let A be the variety of associative algebras over a field K and A = K(x1, . . ., xn) be a free associative algebra in the variety A freely generated by a set X = {x1, . . ., xn}, End A the semigroup of endomorphisms of A, and Aut End A the group of automorphisms of the semigroup End A. We prove that the group Aut End A is generated by semi-inner and mirror automorphisms of End A. A similar result is obtained for the automorphism group Aut ao, where ac is the subcategory of finitely generated free algebras of the variety A. The later result solves Problem 3.9 formulated in [17].

AB - Let A be the variety of associative algebras over a field K and A = K(x1, . . ., xn) be a free associative algebra in the variety A freely generated by a set X = {x1, . . ., xn}, End A the semigroup of endomorphisms of A, and Aut End A the group of automorphisms of the semigroup End A. We prove that the group Aut End A is generated by semi-inner and mirror automorphisms of End A. A similar result is obtained for the automorphism group Aut ao, where ac is the subcategory of finitely generated free algebras of the variety A. The later result solves Problem 3.9 formulated in [17].

KW - Free algebra

KW - Semi-inner automorphism

KW - Variety of associative algebras

UR - http://www.scopus.com/inward/record.url?scp=34748894206&partnerID=8YFLogxK

U2 - 10.1142/s0218196707003901

DO - 10.1142/s0218196707003901

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AN - SCOPUS:34748894206

SN - 0218-1967

VL - 17

SP - 923

EP - 939

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 5-6

ER -