Magento 1 global variable session variable
$session = Mage::getSingleton("core/session");
$session->setData("your_variable", "your value");
// ...
// Now you can retrieve your data elsewhere or even after the next request:
$session = Mage::getSingleton("core/session");
$yourVariable = $session->getData("your_variable"); // will be "your value"
$session->unsetData('your_variable');