If your kernel was compiled with the /proc file system (most are) then you can verify that LVM is present by looking for a /proc/lvm directory. If this doesn't exist then you may have to load the module with the command
# modprobe lvm-mod
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If /proc/lvm still does not exist then check your kernel configuration carefully.
When LVM is active you will see entries in /proc/lvm for all your physical volumes, volume groups and logical volumes. In addition there is a "file" called /proc/lvm/global which gives a summary of the LVM status and also shows just which version of the LVM kernel you are using.