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Page 5649 of Mathematical Reviews Vol. , Issue 94j
[page]

1994
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Mathematical Reviews
*

This interesting paper is a survey (not claiming to be comprehen- sive)

*of*results on endomorphisms*and**automorphisms**of**relatively**free*associative*and**Lie**algebras*over a field K*of*characteristic 0 ... (BG-AOS; Sofia) Endomorphisms*and**automorphisms**of**relatively**free**algebras*. Recent developments in the theory*of**algebras*with polynomial identities (Palermo, 1992). Rend. Circ. Mat. ...##
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Page 694 of American Journal of Mathematics Vol. 82, Issue 4
[page]

1960
*
American Journal of Mathematics
*

Since any

*automorphism**group**of*a*Lie**algebra*induces an isomorphic*automorphism**group**of*any associated simply con- nected*Lie**group**and*every*algebra*has a simply connected, connected associated*Lie*... Step one will consist in showing that there exists an infinite dimensional*Lie**algebra*with*certain*properties. ...##
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Page 5416 of Mathematical Reviews Vol. , Issue 97I
[page]

1997
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Mathematical Reviews
*

The main result

*of*the paper under review is that the [A-*automorphism**group**of*the*relatively**free**algebra*F(V)*of*rank 2 cannot be generated by a finite subset*of*the [A-*automorphism**group**of*F(V) as ... In the case*of*the full*automorphism**group**of**free*metabelian, nilpotent*of*class c*Lie**algebras**of*rank m, V. S. Drenski*and*C. K. Gupta [Canad. J. ...##
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Page 3082 of Mathematical Reviews Vol. , Issue 91F
[page]

1991
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Mathematical Reviews
*

An

*automorphism**of*a*relatively**free**group*is called tame if it is induced by an*automorphism**of*the absolutely*free**group**of*the same rank. ...*of**Lie*type in the same characteristic to morphisms*of**algebraic**groups*. ...##
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A note on free presentations and residual nilpotence

1984
*
Journal of Pure and Applied Algebra
*

Thus it is essentiaily clear that a set

doi:10.1016/0022-4049(84)90023-9
fatcat:iyi5rragezecfloympopkmojta
*of**free*generators*of*the*relatively**free**group*N will generate H freely as a*relatively**free**Lie**algebra*. ... Now we recall some*of*the more elementary parts*of*the Andreev correspondence [2] between*certain*varieties*of**groups**and**Lie**algebras*. ...##
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Page 1055 of Mathematical Reviews Vol. 21, Issue 10
[page]

1960
*
Mathematical Reviews
*

The root system R

*of*the linear*algebraic**group*G is a subset*of*the character*group*X(T)*of*a maximal torus 7*of*G,*and*X(T’) is a*free*abelian*group**of*rank dim 7'. ... T*and*X are*free*abelian*groups**of*rank dim 7’,*and*there exists a nondegenerate pairing*of*[*and*X onto the additive*group**of*integers. ...##
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Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in M_23
[article]

2021
*
arXiv
*
pre-print

Scheithauer showed that there are exactly ten Borcherds-Kac-Moody

arXiv:1905.09629v2
fatcat:udxvi5ftcndmvpbfhuna34ob4q
*algebras*whose denominator identities are completely reflective*automorphic*products*of*singular weight on lattices*of*square-*free*level ... These belong to a larger class*of*Borcherds-Kac-Moody (super)*algebras*Borcherds obtained by twisting the denominator identity*of*the Fake Monster*Lie**algebra*. ... Let ν be*of*square-*free*order m in M 23 . Then the real simple roots*of*g φν are the α ∈ ∆∩d∆ with α, α /2 = d for d | m*and*ρ, α = − α, α /2. ...##
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Anosov Automorphisms of Nilpotent Lie Algebras
[article]

2008
*
arXiv
*
pre-print

Each matrix A in GL_n(Z) naturally defines an

arXiv:0809.3131v1
fatcat:leyve27mpngvncqfuw3zbuwkxq
*automorphism*f*of*the*free*r-step nilpotent*Lie**algebra*on n generators. ... We study the relationship between the matrix A*and*the eigenvalues*and*rational invariant subspaces for f. We give applications to the study*of*Anosov*automorphisms*. ... We can also classify Anosov*Lie**algebras*admitting*automorphisms*whose polynomials p 1 have*certain*specified Galois*groups*. Theorem 1.2. ...##
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Page 4045 of Mathematical Reviews Vol. , Issue 88h
[page]

1988
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Mathematical Reviews
*

Math. 80 (1958), 458-538; MR 21 #1586] studied the relation between irreducible representations

*of*a compact*Lie**group**and**certain**algebraic*homogeneous spaces*of*the*group*. ... Let G be a connected, semisimple*algebraic**group*defined*and*split over Q; let o be an involutive*automorphism*over Q with fixed point*group*H*and*set XY = G/H. ...##
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Page 482 of Mathematical Reviews Vol. 33, Issue 3
[page]

1967
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Mathematical Reviews
*

representations

*of*G,*and*the set*of*G-orbits, in the dual g**of*the*Lie**algebra**of*G. ... , P is a closed characteristic subgroup*of*G,*and*G/P is the direct product*of*a vector*group**and*a discrete torsion-*free*abelian*group*. ...##
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Representation stability for homotopy automorphisms
[article]

2022
*
arXiv
*
pre-print

Under

arXiv:2105.11325v2
fatcat:dejqtkbqi5hf5itvubfyp6lrqy
*certain*conditions on the spaces*and*manifolds, we prove that the rational homotopy*groups**of*these homotopy*automorphisms*form finitely generated FI-modules,*and*thus satisfy representation stability ... We consider in parallel pointed homotopy*automorphisms**of*iterated wedge sums*of*topological spaces*and*boundary*relative*homotopy*automorphisms**of*iterated connected sums*of*manifolds minus a disk. ... Let Aut ι L(H ⊕n , x, y) denote the*group**of*ι-*relative**automorphisms**of*L(H ⊕n , x, y),*and*let ξ : Aut ι L(H ⊕n , x, y) → π 0 (aut ∂ Q (M Q n ) ) be the projection map that sends an ι-*relative**automorphism*...##
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The Pure Braid Groups and Their Relatives
[chapter]

2017
*
Springer INdAM Series
*

We also discuss several natural homomorphisms between these

doi:10.1007/978-3-319-58971-8_15
fatcat:jzxcbxnyvvbh5oebvqjzggag6a
*groups*,*and*various ways to distinguish among the pure braid*groups**and*their*relatives*. ... In this mostly survey paper, we investigate the resonance varieties, the lower central series ranks,*and*the Chen ranks, as well as the residual*and*formality properties*of*several families*of*braid-like ... Braid*groups**and*their*relatives*Braid*groups**and*pure braid*groups*Let Aut(F n ) be the*group**of*(right)*automorphisms**of*the*free**group*F n on generators x 1 , . . . , x n . ...##
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Topological automorphism groups of compact quantum groups
[article]

2017
*
arXiv
*
pre-print

For compact matrix quantum

arXiv:1701.03885v1
fatcat:at23a2qk7nfelhavzqqy7bhty4
*groups*, which can be thought*of*as quantum analogues*of*compact*Lie**groups*, we prove that the inner*automorphism**group*is a compact*Lie**group**and*the outer*automorphism**group*...*group**and**of*the "inner"*automorphism**group*coincide. ... Acknowledgements This work was initiated at the 7th ECM satellite conference "Compact Quantum*Groups*" at Greifswald, Germany*and*the authors are grateful to the organizers, Uwe Franz, Malte Gerhold, Adam ...##
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On Pro-p Groups Admitting a Fixed-Point-Free Automorphism

2000
*
Journal of Algebra
*

ON

doi:10.1006/jabr.1999.8267
fatcat:dx65t3dqdnbxhhwscvzh4e3n2e
*LIE**ALGEBRAS*ADMITTING A FIXED-POINT-*FREE**AUTOMORPHISM*An*automorphism*φ*of*a*Lie**algebra*L is called fixed-point-*free*if C L φ = 0. ... We regard L as a*Lie**algebra*over k ω*and*φ as an*automorphism**of*L. ...##
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Page 764 of Mathematical Reviews Vol. 37, Issue 4
[page]

1969
*
Mathematical Reviews
*

] (which may be, in particular, the category

*of*associative,*Lie*, or commutative associative rings),*and*“ring”*and*“morphism” are meant*relatively*to @. ...*Algebra*9 (1968), 212-219. Let A be a K-supplemented K*algebra*with augmentation ideal A,*and*let A= F/R present A as a*free*associative*algebra*(with unit) modulo an ideal. ...
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