Showing papers in "Siberian Mathematical Journal in 1972"

Remarks on Berger's paper on the domino problem

Abstract: The domino concept was introduced by Hao Wang [2] and is related to the decision problem for the formulas of the predicate calculus with the pref ixAEA (i.e., an existential quantifier between two universal quantifiers). (Also see [3] which, with adequate completeness, presents the resul ts on dominos p r io r to B e r g e r ' s paper . A popularized discuss ion of this question can be found in [4].)

Some examples of Lie groups and Lie algebras

Abstract: We p r e s e n t s o m e e x a m p l e s of l o c a l l y s o l v a b l e s e m i s i m p l e L i e a l g e b r a s tha t a r e not RN* a l g e b r a s , a s w e l l a s e x a m p l e s of l o c a l l y n i lpo ten t RN* L i e a l g e b r a s wi th n e i t h e r Engel e l e m e n t s , nor (of cou r se ) a c c e s s i b l e e l e m e n t s (for de f i n i t i ons , cf. fo r e x a m p l e , [1]-[3]). Ana logous e x a m p l e s w e r e c o n s t r u c t e d for g r o u p s in [4]-[10]. L o c a l l y n i l po t en t RN* L i e a l g e b r a s wi th no Enge l e l e m e n t s w e r e c o n s t r u c t e d in [11]. In th i s p a p e r we w i l l u se a d i f f e r e n t c o n s t r u c t i o n to c r e a t e L i e a l g e b r a s wi th the d e s i r e d p r o p e r t i e s . The b a s e f i e ld 9 wi l l be a r b i t r a r y . We s h a l l show that if a l o c a l l y n i lpo ten t L i e a l g e b r a has a l o c a l l y n i lpo ten t enve lop ing a l g e b r a , then e v e r y e l e m e n t in the o r i g i n a l a l g e b r a i s an Engel e l emen t .