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 -